On associative algebras with unity and Lie index 1

Details On associative algebras with unity and Lie index 1 On associative algebras with unity and Lie index 1

2000-05-16

arxiv.org/abs/math/0005161v2

Mathematics

Rings and Algebras

Removed faulty proof of $V(1)=Stab_F$ at the very end of section 5

Scientific paper

We present a new method of analysis of associative algebras. This method bears a certain resemblance to the famous analysis of commutative $C^*$-algebras in which an important role is played by multiplicative functionals over the algebra. These functionals can be considered as "rank 1" in the framework of our method. In our approach a special position is taken by generic (maximal rank) functionals, which reveal a wealth of information on the structure of non-commutative algebras. We apply this method to derive interesting properties of index of Lie algebras and to analyze finite-dimensional associative algebras with unity and Lie index 1.

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