Description of matrix subalgebras with the given length
Speaker: Dr. Olga Markova (Moscow State University)
Date: Monday, October 20, 2014
Time: 4:00pm
Location: Seminar Room, Ag. 1.01
Abstract:
By the length of a finite system of generators for a finite-dimensional associative algebra over an arbitrary field we mean the least non-negative integer k such that the words in these generators of lengths not exceeding k span this algebra (as a vector space). The maximum length for the systems of generators of an algebra is referred to as the length of the algebra. We consider the question whether the class of matrix subalgebras of a given length can be described up to conjugation or isomorphism and provide some results in the case when the length is close to maximal and minimal values. For example, we describe algebras of length 1 and commutative algebras of lengths n-1 and n-2 in the algebra of matrices of order n.
Series: Algebra and Number Theory
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