Multilinear Algebra over Supersymmetric Rings

✍ Scribed by Andrea Brini; Francesco Regonati; Antonio G.B. Teolis

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 742 KB
• Volume: 145
• Category: Article
• ISSN: 0001-8708
• DOI: 10.1006/aima.1998.1816

✦ Synopsis

Contents

Introduction.

1. Multilinear algebra over a supersymmetric K-algebra. 1-supersymmetric algebras.

A-bimodules. A-linear maps. Tensor products of A-modules. Tensor products of A-linear maps. A-algebras and A-algebra morphisms. A-tensor products of A-algebras. A-coalgebras and A-coalgebra morphisms. A-tensor products of A-coalgebras. A-bialgebras. The antipode. 2. Braiding operators and Yang Baxter equations. Braiding operators. Yang Baxter equations. Admissibility conditions. Twisted tensor products of A-operators.

Twisted tensor products of A-algebras and A-coalgebras. 3. Milnor Moore bialgebras. Milnor Moore A-bialgebras. Twisted tensor product of Milnor Moore A-bialgebras. 4. Scalar extensions. A-scalar extensions of K-operators. Compatible G-gradings.

A-scalar extensions of Hopf K-algebras. 5. Lie algebra actions, derivations, and coderivations. 1-coloured Lie algebras and their representations. The semidirect A-extension of scalars of a Lie superalgebra. The action of a semidirect extension over an A-module. A X as a Lie A (LÄ L)module. Derivations. Coderivations. 6. Lie algebra actions on A-scalar extensions. Lie actions and compatible gradings.

K-derivations on (X, | |, ?) and Lie actions on A X. The Lie action of A (LÄ L) over the algebra A X. K-coderivations on (X, | |, 2) and Lie actions on A X. Lie actions and Hopf A-algebras.