On products of T-ideals in free algebras and free group algebras
A. Yu. Olshanskii
TL;DR
This paper establishes a precise criterion for when a product of T-ideals in free associative or free group algebras is included in another, resolving a question from 1986 through algebraic and representation-theoretic methods.
Contribution
It provides a necessary and sufficient condition for T-ideal inclusion in free algebras, connecting algebraic ideal products with group representation varieties.
Findings
Derived a criterion for T-ideal inclusion in free algebras
Reformulated the problem using group representation varieties
Resolved a longstanding question from 1986
Abstract
Let F be a field and A a free associative F-algebra or a group algebra of a free group with an infinite set X of generators. We find a necessary and sufficient condition for the inclusion I' into I, where I=I_1...I_k and I'=I'_1...I'_l are any products of T-ideals in A. A canonical reformulation in terms of products of group representation varieties answers a question posed in 1986
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory · Advanced Algebra and Logic