Volume: 5, Issue: 3(2006)
pp. 307-332 DOI: 10.1142/S0219498806001740
|
|
Abstract |
Full Text (PDF, 363KB)
|
References
|
 |
| Title: |
THE AMITSUR–LEVITZKI THEOREM FOR THE ORTHOSYMPLECTIC LIE SUPERALGEBRA 𝔬𝔰𝔭(1, 2n) |
| Author(s): |
PIERRE-ALEXANDRE GIÉ
Institut de Mathématiques de Bourgogne, Université de Bourgogne, B.P. 47870, F-21078 Dijon Cedex, FranceGEORGES PINCZON
Institut de Mathématiques de Bourgogne, Université de Bourgogne, B.P. 47870, F-21078 Dijon Cedex, FranceROSANE USHIROBIRA
Institut de Mathématiques de Bourgogne, Université de Bourgogne, B.P. 47870, F-21078 Dijon Cedex, France
|
| History: |
Received 30 November 2004
Accepted 15 February 2005
|
| Abstract: |
Based on Kostant's cohomological interpretation of the Amitsur–Levitzki theorem, we prove a super version of this theorem for the Lie superalgebras 𝔬𝔰𝔭(1, 2n). We conjecture that no other classical Lie superalgebra can satisfy an Amitsur–Levitzki type super identity. We show several (super) identities for the standard super polynomials. Finally, a combinatorial conjecture on the standard skew supersymmetric polynomials is stated. |
| Keywords: |
Lie superalgebras; Amitsur–Levitzki theorem; transgression operator
AMSC numbers:
17B20, 17B56
|
|
|
