메뉴 건너뛰기




Volumn 9, Issue 2, 1999, Pages 179-212

Growth of finitely generated polynilpotent lie algebras and groups, generalized partitions, and functions analytic in the unit circle

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0033453899     PISSN: 02181967     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218196799000138     Document Type: Article
Times cited : (35)

References (53)
  • 5
    • 0345964943 scopus 로고
    • Engl. Transl.
    • A. E. Berezniy, Discrete subexponential groups, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 123 (1983), 155-166; Engl. Transl., J. Soviet Math. 28 (1985), 570-579.
    • (1985) J. Soviet Math. , vol.28 , pp. 570-579
  • 6
    • 0002143661 scopus 로고
    • Basis for free polynilpotent Lie algebras
    • L. A. Bokut', Basis for free polynilpotent Lie algebras, Algebra i Logika 2 (4) (1963), 13-19.
    • (1963) Algebra i Logika , vol.2 , Issue.4 , pp. 13-19
    • Bokut', L.A.1
  • 7
    • 33646971540 scopus 로고
    • Über die Gelfand-Kirillov-Dimension
    • W. Borho and H. Kraft, Über die Gelfand-Kirillov-Dimension, Math. Ann. 220 (1) (1976), 1-24.
    • (1976) Math. Ann. , vol.220 , Issue.1 , pp. 1-24
    • Borho, W.1    Kraft, H.2
  • 8
    • 0003334996 scopus 로고
    • Integral representation and the computation of combinatorial sums
    • Amer. Math. Soc., Providence, RI
    • G. P. Egorychev, Integral representation and the computation of combinatorial sums, Transl. Math. Monogr. Vol. 59, Amer. Math. Soc., Providence, RI, 1984.
    • (1984) Transl. Math. Monogr. , vol.59
    • Egorychev, G.P.1
  • 9
    • 0001023129 scopus 로고
    • Slowly increasing functions and their applications
    • G. A. Fridman, Slowly increasing functions and their applications, Sibirsk. Math. Zh. 7 (5) (1966), 1139-1160.
    • (1966) Sibirsk. Math. Zh. , vol.7 , Issue.5 , pp. 1139-1160
    • Fridman, G.A.1
  • 10
    • 0002021690 scopus 로고
    • Sur les corps lies aux algèbres enveloppantes des algèbres de Lie
    • I. M. Gelfand and A. A. Kirillov, Sur les corps lies aux algèbres enveloppantes des algèbres de Lie, Inst. Hautes Études Sci. Publ. Math. 31 (1966), 509-523.
    • (1966) Inst. Hautes Études Sci. Publ. Math. , vol.31 , pp. 509-523
    • Gelfand, I.M.1    Kirillov, A.A.2
  • 12
    • 0001316024 scopus 로고
    • On Hilbert-Poincaré series of graded algebras associated with groups
    • R. I. Grigorchuk, On Hilbert-Poincaré series of graded algebras associated with groups, Mat. Sb. 180 (2) (1989), 207-225; Engl. Transl. Math. USSR-Sb. 66 (1) (1990), 211229.
    • (1989) Mat. Sb. , vol.180 , Issue.2 , pp. 207-225
    • Grigorchuk, R.I.1
  • 13
    • 0347226225 scopus 로고
    • Engl. Transl.
    • R. I. Grigorchuk, On Hilbert-Poincaré series of graded algebras associated with groups, Mat. Sb. 180 (2) (1989), 207-225; Engl. Transl. Math. USSR-Sb. 66 (1) (1990), 211229.
    • (1990) Math. USSR-Sb. , vol.66 , Issue.1 , pp. 211229
  • 14
    • 0002181076 scopus 로고
    • On growth in group theory
    • Kyoto, Math. Soc. Japan, Tokyo, 1991, 325-338
    • R. I. Grigorchuk, On growth in group theory, Proc. Int. Congress of Math., Vols, I and II (Kyoto, 1990), Math. Soc. Japan, Tokyo, 1991, 325-338.
    • (1990) Proc. Int. Congress of Math. , vol.1-2
    • Grigorchuk, R.I.1
  • 15
    • 0004129399 scopus 로고
    • Chelsea Publishing Co., New York
    • M. Hall, The theory of groups, Chelsea Publishing Co., New York, 1976.
    • (1976) The Theory of Groups
    • Hall, M.1
  • 17
    • 0000412038 scopus 로고
    • The structure of the group ring of a p-group over a modular field
    • S. A. Jennings, The structure of the group ring of a p-group over a modular field, Trans. Amer. Math. Soc. 50 (1941), 175-185.
    • (1941) Trans. Amer. Math. Soc. , vol.50 , pp. 175-185
    • Jennings, S.A.1
  • 18
    • 84972494018 scopus 로고
    • An asymptotic formula for Cayley's double partition function p(2;n)
    • R. Kaneiwa, An asymptotic formula for Cayley's double partition function p(2;n), Tokyo. J. Math. 2 (1) (1979), 137-158.
    • (1979) Tokyo. J. Math. , vol.2 , Issue.1 , pp. 137-158
    • Kaneiwa, R.1
  • 21
    • 0001524188 scopus 로고
    • Sur les groupes nilpotents et les anneaux de Lie
    • M. Lazard, Sur les groupes nilpotents et les anneaux de Lie, Ann. Sci. École Norm. Sup. 71 (1954), 101-190.
    • (1954) Ann. Sci. École Norm. Sup. , vol.71 , pp. 101-190
    • Lazard, M.1
  • 22
    • 51249180407 scopus 로고
    • Growth in enveloping algebras
    • A. I. Lichtman, Growth in enveloping algebras, Israel J. Math. 47 (4) (1984), 297-304.
    • (1984) Israel J. Math. , vol.47 , Issue.4 , pp. 297-304
    • Lichtman, A.I.1
  • 23
    • 0011650185 scopus 로고
    • On growth of some algebras of vector fields
    • A. I. Molev, On growth of some algebras of vector fields, Uspekhi Mat. Nauk 41 (2) (1986), 205-206; Engl. Transl. Russian Math. Surveys, 41 (2) (1986), 213-214.
    • (1986) Uspekhi Mat. Nauk , vol.41 , Issue.2 , pp. 205-206
    • Molev, A.I.1
  • 24
    • 84956230080 scopus 로고
    • Engl. Transl.
    • A. I. Molev, On growth of some algebras of vector fields, Uspekhi Mat. Nauk 41 (2) (1986), 205-206; Engl. Transl. Russian Math. Surveys, 41 (2) (1986), 213-214.
    • (1986) Russian Math. Surveys , vol.41 , Issue.2 , pp. 213-214
  • 25
    • 0003241384 scopus 로고
    • Group rings and their augmentation ideals
    • Springer-Verlag, Berlin/Heidelberg/New York
    • I. B. S. Passi, Group rings and their augmentation ideals, Lecture Notes in Mathematics, 715, Springer-Verlag, Berlin/Heidelberg/New York, 1979.
    • (1979) Lecture Notes in Mathematics , vol.715
    • Passi, I.B.S.1
  • 26
    • 0000758123 scopus 로고
    • On some types of intermediate growth in Lie algebras
    • V. M. Petrogradsky, On some types of intermediate growth in Lie algebras, Uspekhi Mat. Nauk 48 (5) (1993), 181-182; Engl. Transl. Russian Math. Surveys 48 (5) (1993), 181-182.
    • (1993) Uspekhi Mat. Nauk , vol.48 , Issue.5 , pp. 181-182
    • Petrogradsky, V.M.1
  • 27
    • 84892644796 scopus 로고
    • Engl. Transl.
    • V. M. Petrogradsky, On some types of intermediate growth in Lie algebras, Uspekhi Mat. Nauk 48 (5) (1993), 181-182; Engl. Transl. Russian Math. Surveys 48 (5) (1993), 181-182.
    • (1993) Russian Math. Surveys , vol.48 , Issue.5 , pp. 181-182
  • 28
    • 0001326417 scopus 로고
    • On types of overexponential growth of identities in Lie PI-algebras
    • V. M. Petrogradsky, On types of overexponential growth of identities in Lie PI-algebras, Fundamentalnaya i Prikladnaya Matematika 1 (4) (1995), 989-1007.
    • (1995) Fundamentalnaya i Prikladnaya Matematika , vol.1 , Issue.4 , pp. 989-1007
    • Petrogradsky, V.M.1
  • 29
    • 0030584068 scopus 로고    scopus 로고
    • Intermediate growth in Lie algebras and their enveloping algebras
    • V. M. Petrogradsky, Intermediate growth in Lie algebras and their enveloping algebras, J. Algebra 179 (1996), 459-482.
    • (1996) J. Algebra , vol.179 , pp. 459-482
    • Petrogradsky, V.M.1
  • 30
    • 0347226226 scopus 로고    scopus 로고
    • Growth in polynilpotent Lie algebras
    • Miskols, Hungary, July
    • V. M. Petrogradsky, Growth in polynilpotent Lie algebras, Thesises of Ring Theory Conference, Miskols, Hungary, July 1996, 46-47.
    • (1996) Thesises of ring Theory Conference , pp. 46-47
    • Petrogradsky, V.M.1
  • 31
    • 21744444238 scopus 로고    scopus 로고
    • On Lie Algebras with nonintegral q-dimensions
    • V. M. Petrogradsky, On Lie Algebras with nonintegral q-dimensions, Proc. Amer. Math. Soc. 125 (3) (1997), 649-656.
    • (1997) Proc. Amer. Math. Soc. , vol.125 , Issue.3 , pp. 649-656
    • Petrogradsky, V.M.1
  • 32
    • 0031286541 scopus 로고    scopus 로고
    • Growth of polynilpotent varieties of Lie algebras and rapidly growing entire functions
    • V. M. Petrogradsky, Growth of polynilpotent varieties of Lie algebras and rapidly growing entire functions, Mat. Sb. 188 (6) (1997), 119-138; Engl. Transl. Russian Acad. Sci. Sb. Math. 188 (6) (1997), 913-931.
    • (1997) Mat. Sb. , vol.188 , Issue.6 , pp. 119-138
    • Petrogradsky, V.M.1
  • 33
    • 0031286541 scopus 로고    scopus 로고
    • Engl. Transl.
    • V. M. Petrogradsky, Growth of polynilpotent varieties of Lie algebras and rapidly growing entire functions, Mat. Sb. 188 (6) (1997), 119-138; Engl. Transl. Russian Acad. Sci. Sb. Math. 188 (6) (1997), 913-931.
    • (1997) Russian Acad. Sci. Sb. Math. , vol.188 , Issue.6 , pp. 913-931
  • 34
    • 0006388969 scopus 로고
    • Introduction to analytic number theory
    • Amer. Math. Soc., Providence, RI
    • A. G. Postnikov, Introduction to analytic number theory, Transl. Math. Monogr. Vol. 68, Amer. Math. Soc., Providence, RI, 1988.
    • (1988) Transl. Math. Monogr. , vol.68
    • Postnikov, A.G.1
  • 35
    • 0141556464 scopus 로고
    • Tauberian theory and its applications
    • A. G. Postnikov, Tauberian theory and its applications, Trudy Mat. Inst. Steklov., Vol. 144 (1979); English Transl. Proc. Steklov. Inst. Math. (2) (1980).
    • (1979) Trudy Mat. Inst. Steklov. , vol.144
    • Postnikov, A.G.1
  • 36
    • 0346596351 scopus 로고
    • English Transl.
    • A. G. Postnikov, Tauberian theory and its applications, Trudy Mat. Inst. Steklov., Vol. 144 (1979); English Transl. Proc. Steklov. Inst. Math. (2) (1980).
    • (1980) Proc. Steklov. Inst. Math. , Issue.2
  • 38
    • 84966230389 scopus 로고
    • Existence of polynomial identities in A ⊗ B
    • A. Regev, Existence of polynomial identities in A ⊗ B, Bull. Amer. Math. Soc. 77 (6) (1971), 1067-1069.
    • (1971) Bull. Amer. Math. Soc. , vol.77 , Issue.6 , pp. 1067-1069
    • Regev, A.1
  • 41
    • 0004174102 scopus 로고
    • Introduction in complex analysis
    • Amer. Math. Soc., Providence, RI
    • B. V. Shabat, Introduction in complex analysis, Transl. Math. Monogr., Amer. Math. Soc., Providence, RI, 1992.
    • (1992) Transl. Math. Monogr.
    • Shabat, B.V.1
  • 42
    • 0002034917 scopus 로고
    • Free polynilpotent groups
    • A. L. Shmel'kin, Free polynilpotent groups, Izv. Akad. Nauk SSSR Ser. Mat. 28 (1) (1964), 91-122; English Transl. Amer. Math. Soc. Transl. Ser. 2, Vol. 55, Amer. Math. Soc., Providence, RI (1966), 270-304.
    • (1964) Izv. Akad. Nauk SSSR Ser. Mat. , vol.28 , Issue.1 , pp. 91-122
    • Shmel'kin, A.L.1
  • 43
    • 28044432061 scopus 로고
    • English Transl. Amer. Math. Soc., Providence, RI
    • A. L. Shmel'kin, Free polynilpotent groups, Izv. Akad. Nauk SSSR Ser. Mat. 28 (1) (1964), 91-122; English Transl. Amer. Math. Soc. Transl. Ser. 2, Vol. 55, Amer. Math. Soc., Providence, RI (1966), 270-304.
    • (1966) Amer. Math. Soc. Transl. Ser. 2 , vol.55 , pp. 270-304
  • 44
    • 84968490629 scopus 로고
    • Universal enveloping algebras with subexponential but not polynomially bounded growth
    • M. K. Smith, Universal enveloping algebras with subexponential but not polynomially bounded growth, Proc. Amer. Math. Soc. 60 (1976), 22-24.
    • (1976) Proc. Amer. Math. Soc. , vol.60 , pp. 22-24
    • Smith, M.K.1
  • 46
    • 0002547755 scopus 로고
    • Combinatorial and asymptotic methods in algebra
    • Moscow
    • V. A. Ufnarovskiy, Combinatorial and asymptotic methods in algebra, Itogi Nauki i Tekhniki, Sovrem. Probl. Mat. Fund. Naprav. Vol. 57, Moscow, 1989; Engl. Transl. Encyclopaedia Math. Sci., Vol. 57, Algebra VI, Springer, Berlin, 1995.
    • (1989) Itogi Nauki i Tekhniki, Sovrem. Probl. Mat. Fund. Naprav. , vol.57
    • Ufnarovskiy, V.A.1
  • 47
    • 0004154142 scopus 로고
    • Engl. Transl. Algebra VI, Springer, Berlin
    • V. A. Ufnarovskiy, Combinatorial and asymptotic methods in algebra, Itogi Nauki i Tekhniki, Sovrem. Probl. Mat. Fund. Naprav. Vol. 57, Moscow, 1989; Engl. Transl. Encyclopaedia Math. Sci., Vol. 57, Algebra VI, Springer, Berlin, 1995.
    • (1995) Encyclopaedia Math. Sci. , vol.57
  • 49
    • 0347856368 scopus 로고
    • Engl. Transl.
    • V. A. Ufnarovskiy, On growth of algebras, Vestnik Moskov. Univ. Ser. I Mat. Mekh. (4) (1978), 59-65; Engl. Transl. Moscow Univ. Math. Bull. 33 (4) (1978), 47-52.
    • (1978) Moscow Univ. Math. Bull. , vol.33 , Issue.4 , pp. 47-52
  • 51
    • 0000531719 scopus 로고
    • 2 over field of zero characteristic
    • 2 over field of zero characteristic, Dokl. Akad. Nauk Belarusi XXV (12) (1981), 1063-1066.
    • (1981) Dokl. Akad. Nauk Belarusi , vol.25 , Issue.12 , pp. 1063-1066
    • Volichenko, I.B.1
  • 52
    • 0003178334 scopus 로고
    • Ein Verfahren jeder endlichen p-Gruppe einen Lie-Ring mit der Charakteristik p zuzuordnen
    • H. Zassenhaus, Ein Verfahren jeder endlichen p-Gruppe einen Lie-Ring mit der Charakteristik p zuzuordnen, Abh. Math. Sem. Univ. Hamburg 13 (1940), 200-207.
    • (1940) Abh. Math. Sem. Univ. Hamburg , vol.13 , pp. 200-207
    • Zassenhaus, H.1
  • 53
    • 0000815484 scopus 로고
    • On the restricted Burnside problem
    • Kyoto, Math. Soc. Japan, Tokyo
    • E. I. Zelmanov, On the restricted Burnside problem, Proc. Int. Congress of Math. Vols. I and II (Kyoto, 1990), 395-402, Math. Soc. Japan, Tokyo, 1991.
    • (1990) Proc. Int. Congress of Math. , vol.1-2 , pp. 395-402
    • Zelmanov, E.I.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.