2000/05/16 by Vladimir Dergachev, Dergachev, Vladimir
Mathematics · #16B99 #17B99 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.RA #math.RT #msc:16B99 #msc:17B99
paper · pdf · doi:10.48550/arxiv.math/0005161
Removed faulty proof of $V(1)=Stab_F$ at the very end of section 5
openalex publication_date 2000/05/16 · arxiv created 2001/08/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.