On boson algebras as Hopf algebras

Journal of Physics A: Mathematical and General

Volumn 30, Issue 11, 1997, Pages 4075-4087

  Tsohantjis, I ^a   Paolucci, A ^b   Jarvis, P D ^a  

^a UNIVERSITY OF TASMANIA   (Australia)

^b UNIVERSITY OF LEEDS   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031557985     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/30/11/032     Document Type: Article

References (77)

1. Drinfeld V G 1986 Quantum Groups Proc. ICM Berkeley 1 798
2. Jimbo M 1985 Lett. Math. Phys. 10 63 Jimbo M 1986 Lett. Math. Phys. 11 247 Jimbo M 1987 Commun. Math. Phys. 102 537 Jimbo M 1990 Quantum groups Proc. Argonne Workshop ed T Curtright, D Fairlie and C Zachos (Singapore: World Scientific)
3. Jimbo M 1985 Lett. Math. Phys. 10 63 Jimbo M 1986 Lett. Math. Phys. 11 247 Jimbo M 1987 Commun. Math. Phys. 102 537 Jimbo M 1990 Quantum groups Proc. Argonne Workshop ed T Curtright, D Fairlie and C Zachos (Singapore: World Scientific)
4. Jimbo M 1985 Lett. Math. Phys. 10 63 Jimbo M 1986 Lett. Math. Phys. 11 247 Jimbo M 1987 Commun. Math. Phys. 102 537 Jimbo M 1990 Quantum groups Proc. Argonne Workshop ed T Curtright, D Fairlie and C Zachos (Singapore: World Scientific)
5. Jimbo M 1985 Lett. Math. Phys. 10 63 Jimbo M 1986 Lett. Math. Phys. 11 247 Jimbo M 1987 Commun. Math. Phys. 102 537 Jimbo M 1990 Quantum groups Proc. Argonne Workshop ed T Curtright, D Fairlie and C Zachos (Singapore: World Scientific)
6. Woronowicz S L 1987 Commun. Math. Phys. 111 613 Woronowicz S L 1987 Publ. RIMS 23 117-81 Woronowicz S L 1988 Inv. Math. 93 35
7. Woronowicz S L 1987 Commun. Math. Phys. 111 613 Woronowicz S L 1987 Publ. RIMS 23 117-81 Woronowicz S L 1988 Inv. Math. 93 35
8. Woronowicz S L 1987 Commun. Math. Phys. 111 613 Woronowicz S L 1987 Publ. RIMS 23 117-81 Woronowicz S L 1988 Inv. Math. 93 35
9. Links R J and Gould M D 1992 Rep. Math. Phys. 31 91 Gould M D, Zhang R B and Bracken A J 1991 J. Math. Phys. 32 2298
10. Links R J and Gould M D 1992 Rep. Math. Phys. 31 91 Gould M D, Zhang R B and Bracken A J 1991 J. Math. Phys. 32 2298
11. Vyjayanthi Chari and Pressley A 1995 A Guide to Quantum Groups (Melbourne: Cambridge University Press)
12. Gould M D, Zhang R B and Bracken A J 1993 Bull. Austral. Math. Soc. 47 353 Khoroshkin S M and Tolstoy V N 1991 Commun. Math. Phys. 141 599 Kulish P P Reshetikhin N Y 1989 Lett. Math. Phys. 18 143 Bracken A J, Gould M D and Tsohantjis I 1993 J. Math. Phys. 34 1654 Bracken A J, Gould M D and Zhang R B 1990 Mod. Phys. Lett. A 5 831 Links R J, Scheunert M and Gould M D 1994 Lett. Math. Phys. 32 231 Zhang R B 1993 J. Math. Phys. 34 1236 Zhang R B 1993 J. Phys. A: Math. Gen. 26 7041
13. Gould M D, Zhang R B and Bracken A J 1993 Bull. Austral. Math. Soc. 47 353 Khoroshkin S M and Tolstoy V N 1991 Commun. Math. Phys. 141 599 Kulish P P Reshetikhin N Y 1989 Lett. Math. Phys. 18 143 Bracken A J, Gould M D and Tsohantjis I 1993 J. Math. Phys. 34 1654 Bracken A J, Gould M D and Zhang R B 1990 Mod. Phys. Lett. A 5 831 Links R J, Scheunert M and Gould M D 1994 Lett. Math. Phys. 32 231 Zhang R B 1993 J. Math. Phys. 34 1236 Zhang R B 1993 J. Phys. A: Math. Gen. 26 7041
14. Gould M D, Zhang R B and Bracken A J 1993 Bull. Austral. Math. Soc. 47 353 Khoroshkin S M and Tolstoy V N 1991 Commun. Math. Phys. 141 599 Kulish P P Reshetikhin N Y 1989 Lett. Math. Phys. 18 143 Bracken A J, Gould M D and Tsohantjis I 1993 J. Math. Phys. 34 1654 Bracken A J, Gould M D and Zhang R B 1990 Mod. Phys. Lett. A 5 831 Links R J, Scheunert M and Gould M D 1994 Lett. Math. Phys. 32 231 Zhang R B 1993 J. Math. Phys. 34 1236 Zhang R B 1993 J. Phys. A: Math. Gen. 26 7041
15. Gould M D, Zhang R B and Bracken A J 1993 Bull. Austral. Math. Soc. 47 353 Khoroshkin S M and Tolstoy V N 1991 Commun. Math. Phys. 141 599 Kulish P P Reshetikhin N Y 1989 Lett. Math. Phys. 18 143 Bracken A J, Gould M D and Tsohantjis I 1993 J. Math. Phys. 34 1654 Bracken A J, Gould M D and Zhang R B 1990 Mod. Phys. Lett. A 5 831 Links R J, Scheunert M and Gould M D 1994 Lett. Math. Phys. 32 231 Zhang R B 1993 J. Math. Phys. 34 1236 Zhang R B 1993 J. Phys. A: Math. Gen. 26 7041
16. Gould M D, Zhang R B and Bracken A J 1993 Bull. Austral. Math. Soc. 47 353 Khoroshkin S M and Tolstoy V N 1991 Commun. Math. Phys. 141 599 Kulish P P Reshetikhin N Y 1989 Lett. Math. Phys. 18 143 Bracken A J, Gould M D and Tsohantjis I 1993 J. Math. Phys. 34 1654 Bracken A J, Gould M D and Zhang R B 1990 Mod. Phys. Lett. A 5 831 Links R J, Scheunert M and Gould M D 1994 Lett. Math. Phys. 32 231 Zhang R B 1993 J. Math. Phys. 34 1236 Zhang R B 1993 J. Phys. A: Math. Gen. 26 7041
17. Gould M D, Zhang R B and Bracken A J 1993 Bull. Austral. Math. Soc. 47 353 Khoroshkin S M and Tolstoy V N 1991 Commun. Math. Phys. 141 599 Kulish P P Reshetikhin N Y 1989 Lett. Math. Phys. 18 143 Bracken A J, Gould M D and Tsohantjis I 1993 J. Math. Phys. 34 1654 Bracken A J, Gould M D and Zhang R B 1990 Mod. Phys. Lett. A 5 831 Links R J, Scheunert M and Gould M D 1994 Lett. Math. Phys. 32 231 Zhang R B 1993 J. Math. Phys. 34 1236 Zhang R B 1993 J. Phys. A: Math. Gen. 26 7041
18. Gould M D, Zhang R B and Bracken A J 1993 Bull. Austral. Math. Soc. 47 353 Khoroshkin S M and Tolstoy V N 1991 Commun. Math. Phys. 141 599 Kulish P P Reshetikhin N Y 1989 Lett. Math. Phys. 18 143 Bracken A J, Gould M D and Tsohantjis I 1993 J. Math. Phys. 34 1654 Bracken A J, Gould M D and Zhang R B 1990 Mod. Phys. Lett. A 5 831 Links R J, Scheunert M and Gould M D 1994 Lett. Math. Phys. 32 231 Zhang R B 1993 J. Math. Phys. 34 1236 Zhang R B 1993 J. Phys. A: Math. Gen. 26 7041
19. Gould M D, Zhang R B and Bracken A J 1993 Bull. Austral. Math. Soc. 47 353 Khoroshkin S M and Tolstoy V N 1991 Commun. Math. Phys. 141 599 Kulish P P Reshetikhin N Y 1989 Lett. Math. Phys. 18 143 Bracken A J, Gould M D and Tsohantjis I 1993 J. Math. Phys. 34 1654 Bracken A J, Gould M D and Zhang R B 1990 Mod. Phys. Lett. A 5 831 Links R J, Scheunert M and Gould M D 1994 Lett. Math. Phys. 32 231 Zhang R B 1993 J. Math. Phys. 34 1236 Zhang R B 1993 J. Phys. A: Math. Gen. 26 7041
20. Arik M and Coon D D 1976 J. Math. Phys. 17 524
21. Macfarlane A J 1989 J. Phys. A: Math. Gen. 22 4581
22. Biedenharn L C 1989 J. Phys. A: Math. Gen. 22 L873
23. Sun C-P and Fu H-C 1989 J. Phys. A: Math. Gen. 22 L983
24. Chakrabarti R and Jaganathan R 1991 J. Phys. A: Math. Gen. 24 L111
25. Vasiliev M A 1989 Pis. - JETP 50 344 Vasiliev M A 1991 Int. J. Mod. Phys. A 6 1115
26. Vasiliev M A 1989 Pis. - JETP 50 344 Vasiliev M A 1991 Int. J. Mod. Phys. A 6 1115
27. Brzezinski T, Egusquiza I L and Macfarlane A J 1993 Phys. Lett. B 311 202
28. Macfarlane A J 1994 J. Math. Phys. 35 1054
29. Kuryshkin W 1980 Ann. Found. L de Broglie 5 111
30. Jannussis A et al 1982 Hadronic J. 5 1923 Jannussis A, Brodimas G, Sourlas D and Zisis V 1981 Lett. Nuovo Cimento 30 123 Jannussis A 1991 Hadronic J. 14 257 Brodimas G 1991 Lie admissible Q-algebras and quantum groups PhD Thesis University of Patras
31. Jannussis A et al 1982 Hadronic J. 5 1923 Jannussis A, Brodimas G, Sourlas D and Zisis V 1981 Lett. Nuovo Cimento 30 123 Jannussis A 1991 Hadronic J. 14 257 Brodimas G 1991 Lie admissible Q-algebras and quantum groups PhD Thesis University of Patras
32. Jannussis A et al 1982 Hadronic J. 5 1923 Jannussis A, Brodimas G, Sourlas D and Zisis V 1981 Lett. Nuovo Cimento 30 123 Jannussis A 1991 Hadronic J. 14 257 Brodimas G 1991 Lie admissible Q-algebras and quantum groups PhD Thesis University of Patras
33. Jannussis A et al 1982 Hadronic J. 5 1923 Jannussis A, Brodimas G, Sourlas D and Zisis V 1981 Lett. Nuovo Cimento 30 123 Jannussis A 1991 Hadronic J. 14 257 Brodimas G 1991 Lie admissible Q-algebras and quantum groups PhD Thesis University of Patras
34. Ng Y T 1990 J. Phys. A: Math. Gen. 23 1023
35. Kulish P P and Damaskinsky E V 1990 J. Phys. A: Math. Gen. 23 L415
36. Chaichian M and Kulish P P 1990 Phys. Lett. B 234 72
37. Chaichian M and Ellinas D 1990 J. Phys. A: Math. Gen. 23 L291
38. Chaichian M, Kulish P P and Lukierski J 1990 Phys. Lett. B 237 401
39. Sun Chang-Pu and Ge Mo-Lin 1991 J. Math. Phys. 32 595
40. Oh C H and Singh K 1994 J. Phys. A: Math. Gen. 27 5907
41. Cho K-H and Park S U 1995 J. Phys. A: Math. Gen. 28 1005
42. Daskaloyannis C 1991 J. Phys. A: Math. Gen. 24 L789
43. Bracken A J, McAnally D S, Zhang R B and Gould M D 1991 J. Phys. A: Math. Gen. 24 1379
44. McDermott R J and Solomon 1994 J. Phys. A: Math. Gen. 24 L15
45. Katriel J and Quesne C 1996 J. Math. Phys. 37 1650
46. Plyushchay M S 1994 Phys. Lett. B 320 91 Plyushchay M S 1996 Ann. Phys. 245 339
47. Plyushchay M S 1994 Phys. Lett. B 320 91 Plyushchay M S 1996 Ann. Phys. 245 339
48. Plyushchay M S 1996 Ann. Phys. 245 339
49. Brink L, Hansson T H and Vasiliev M A 1992 Phys. Lett. B 286 109 Brink L, Hansson T H, Konstein S and Vasiliev M A 1993 Nucl. Phys. B 401 591
50. Brink L, Hansson T H and Vasiliev M A 1992 Phys. Lett. B 286 109 Brink L, Hansson T H, Konstein S and Vasiliev M A 1993 Nucl. Phys. B 401 591
51. Calogero F 1969 J. Math. Phys. 10 2191 Calogero F 1971 J. Math. Phys. 12 419 Sutherland B 1971 J. Math. Phys. 12 246
52. Calogero F 1969 J. Math. Phys. 10 2191 Calogero F 1971 J. Math. Phys. 12 419 Sutherland B 1971 J. Math. Phys. 12 246
53. Calogero F 1969 J. Math. Phys. 10 2191 Calogero F 1971 J. Math. Phys. 12 419 Sutherland B 1971 J. Math. Phys. 12 246
54. Calogero F 1995 Phys. Lett. A 201 306 Calogero F 1995 J. Math. Phys. 36 9 Calogero F and van Diejen J F 1995 Phys. Lett. A 205 143
55. Calogero F 1995 Phys. Lett. A 201 306 Calogero F 1995 J. Math. Phys. 36 9 Calogero F and van Diejen J F 1995 Phys. Lett. A 205 143
56. Calogero F 1995 Phys. Lett. A 201 306 Calogero F 1995 J. Math. Phys. 36 9 Calogero F and van Diejen J F 1995 Phys. Lett. A 205 143
57. Jørgensen P E T, Schmitt L M and Werner R F 1994 Pacific J. Math. 165 131
58. Jørgensen P E T, Schmitt L M and Werner R F 1995 J. Funct. Anal. 134 33
59. Jørgensen P E T, Schmitt L M and Werner R F 1994 q-relations and Stability of C*-isomorphism Classes in Algebraic Methods in Operator Theory ed R Curto and P E T Jørgensen (Boston, MA: Birkhäuser)
60. Jørgensen P E T 1994 Contemp. Math. 160 141
61. Jørgensen P E T and Werner R F 1994 Commun. Math. Phys. 164 455
62. Chaichian M, Grosse H and Presnajder 1994 J. Phys. A: Math. Gen. 27 2045 Chaichian M, Gonzalez Felipe R and Presnajder 1995 J. Phys. A: Math. Gen. 28 2247
63. Chaichian M, Grosse H and Presnajder 1994 J. Phys. A: Math. Gen. 27 2045 Chaichian M, Gonzalez Felipe R and Presnajder 1995 J. Phys. A: Math. Gen. 28 2247
64. q(n) to a Hopf algebra? Preprint ICTP, Trieste IC-93-163 hep-th/9307032
65. Hong Yan 1990 J. Phys. A: Math. Gen. 23 L1155
66. Jian-Hui Dai, Han-Ying Guo and Hong Yan 1991 J. Phys. A: Math. Gen. 24 L409
67. Hong Yan 1991 Phys. Lett. B 262 459
68. McAnally D S and Tsohantjis I 1997 J. Phys. A: Math. Gen. 30 651
69. Paolucci A and Tsohantjis I On Hopf-type boson algebras and their fixed point subalgebras, in preparation
70. Macfarlane A J and Majid S 1992 Int. J. Mod. Phys. A 7 4377
71. Sweedler M E 1969 Hopf Algebras (New York: Benjamin)
72. Bracken A J and Leemon H I 1980 J. Math. Phys. 21 2170 Bracken A J and Leemon H I 1981 J. Math. Phys. 22 719 Jarvis P D and Baker T H 1992 J. Phys. A: Math. Gen. 26 883 Jarvis P D, Warner R C, Yung C M and Zhang R B 1992 J. Phys. A: Math. Gen. 25 L895-900
73. Bracken A J and Leemon H I 1980 J. Math. Phys. 21 2170 Bracken A J and Leemon H I 1981 J. Math. Phys. 22 719 Jarvis P D and Baker T H 1992 J. Phys. A: Math. Gen. 26 883 Jarvis P D, Warner R C, Yung C M and Zhang R B 1992 J. Phys. A: Math. Gen. 25 L895-900
74. Bracken A J and Leemon H I 1980 J. Math. Phys. 21 2170 Bracken A J and Leemon H I 1981 J. Math. Phys. 22 719 Jarvis P D and Baker T H 1992 J. Phys. A: Math. Gen. 26 883 Jarvis P D, Warner R C, Yung C M and Zhang R B 1992 J. Phys. A: Math. Gen. 25 L895-900
75. Bracken A J and Leemon H I 1980 J. Math. Phys. 21 2170 Bracken A J and Leemon H I 1981 J. Math. Phys. 22 719 Jarvis P D and Baker T H 1992 J. Phys. A: Math. Gen. 26 883 Jarvis P D, Warner R C, Yung C M and Zhang R B 1992 J. Phys. A: Math. Gen. 25 L895-900
76. Tsohantjis I, Jarvis P D and Paolucci A 1996 Oscillator algebras as Hopf algebras Poster Presented at the 12th Australian Institute of Physics Congress (Hobart, 1-5 July) Paolucci A and Tsohantjis I 1996 Hopf-type deformed oscillators, their quantum double and a q-deformed Calogero-Vasiliev algebra Talk Presented at the 3rd Int. Conf. on Functional Analysis and Approximation Theory (23-28 September, Acquafredda di Maratea, Potenza, Italy) submitted
77. Tsohantjis I, Jarvis P D and Paolucci A 1996 Oscillator algebras as Hopf algebras Poster Presented at the 12th Australian Institute of Physics Congress (Hobart, 1-5 July) Paolucci A and Tsohantjis I 1996 Hopf-type deformed oscillators, their quantum double and a q-deformed Calogero-Vasiliev algebra Talk Presented at the 3rd Int. Conf. on Functional Analysis and Approximation Theory (23-28 September, Acquafredda di Maratea, Potenza, Italy) submitted