Nonhomogeneous subalgebras of Lie and special Jordan superalgebras
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- 作者：Murray R. Bremner ; Luiz A. Peresi
- 关键词：Lie superalgebras ; Special Jordan superalgebras ; Nonhomogeneous subalgebras ; Polynomial identities ; Computational algebra
- 刊名：Journal of Algebra
- 出版年：2009
- 出版时间：15 September 2009
- 年：2009
- 卷：322
- 期：6
- 页码：2000-2026
- 全文大小：301 K
文摘
We consider polynomial identities satisfied by nonhomogeneous subalgebras of Lie and special Jordan superalgebras: we ignore the grading and regard the superalgebra as an ordinary algebra. The Lie case has been studied by Volichenko and Baranov: they found identities in degrees 3, 4 and 5 which imply all the identities in degrees 6. We simplify their identities in degree 5, and show that there are no new identities in degree 7. The Jordan case has not previously been studied: we find identities in degrees 3, 4, 5 and 6 which imply all the identities in degrees 6, and demonstrate the existence of further new identities in degree 7. Our proofs depend on computer algebra; we use the representation theory of the symmetric group, the Hermite normal form of an integer matrix, the LLL algorithm for lattice basis reduction, and the Chinese remainder theorem.