Sur une algèbre Q-symétrique

• Autorzy: A. Guichardet
• Języki publikacji: FR

Abstrakty

FR

We establish several properties of a quadratic algebra over a field k, which is a deformation of the symmetric algebra Sk³. In particular, we prove that A is an integral domain, noetherian and Koszul; we compute its first Hochschild cohomology group; we determine the corresponding Poisson structure on k³ and its symplectic leaves; we define an involution on A and describe the corresponding irreducible involutive representations.

Słowa kluczowe

FR

deformations; derivations; symplectic leaves; representations

Kategorie tematyczne

• 18G15: Ext and Tor, generalizations, K\"unneth formula
• 16W10: Rings with involution; Lie, Jordan and other nonassociative structures

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1997
• Tom: 66
• Numer: 1
• Strony: 123-135

Daty

wydano

1997

otrzymano

1995-09-01

Twórcy

autor

A. Guichardet

• Centre de Mathématiques, École Polytechnique, 91128 Palaiseau, France

Bibliografia

• [1] J. Alev et M. Chamarie, Dérivations et automorphismes de quelques algèbres quantiques, Comm. Algebra 20 (1992), 1787-1802.
• [2] A. Beilinson, V. Ginzburg and W. Soergel, Koszul duality patterns in representation theory, J. Amer. Math. Soc. 9 (1996), 473-527.
• [3] E. Celeghini, R. Giachetti, E. Sorace and M. Tarlini, The 3-dimensional Euclidean quantum group $E(3)_q$ and its R-matrix, J. Math. Phys. 32 (1991), 1159-1165.
• [4] V. Chari and A. Pressley, A Guide to Quantum Groups, Cambridge Univ. Press, 1994.
• [5] A. Guichardet, Groupes quantiques, InterEditions, 1995.
• [6] C. Kassel, Quantum Groups, Springer, 1995.
• [7] R. K. Molnar, Semi-direct products of Hopf algebras, J. Algebra 47 (1977), 29-51.
• [8] Ya. S. Soĭbel'man, The algebra of functions on a compact quantum group and its representations, Algebra i Analiz 2 (1) (1990), 190-212 (in Russian); English transl.: Leningrad Math. J. 2 (1) (1991), 161-178.
• [9] L. L. Vaksman and Y. S. Soĭbel'man, An algebra of functions on the quantum group SU(2), Funktsional. Anal. i Prilozhen. 22 (3) (1988), 1-14 (in Russian); English transl.: Funct. Anal. Appl. 22 (3) (1988), 170-181.
• [10] M. Van den Bergh, Noncommutative homology of some 3-dimensional quantum spaces, K-Theory 8 (1994), 213-230.
• [11] M. Wambst, Complexes de Koszul quantiques, Ann. Inst. Fourier (Grenoble) 43 (1993), 1089-1156.
• [12] S. L. Woronowicz, Quantum E(2) group and its Pontryagin dual, Lett. Math. Phys. 23 (1991), 251-263.