Reduction techniques for the finitistic dimension
Copyright policy )Reduction techniques for the finitistic dimension
In this paper we develop new reduction techniques for testing the finiteness of the finitistic dimension of a finite dimensional algebra over a field. Viewing the latter algebra as a quotient of a path algebra, we propose two operations on the quiver of the algebra, namely arrow removal and vertex removal. The former gives rise to cleft extensions and the latter to recollements. These two operations provide us new practical methods to detect algebras of finite finitistic dimension. We illustrate our methods with many examples.
- Department of Mathematical Sciences Russian Federation
- Virginia Tech United States
- Aristotle University of Thessaloniki Greece
- Norwegian University of Science and Technology Norway
path algebras, Homological dimension in associative algebras, Mathematics - Category Theory, Mathematics - Rings and Algebras, Homological dimension (category-theoretic aspects), recollements of abelian categories, Rings and Algebras (math.RA), Abelian categories, Grothendieck categories, cleft extension of abelian categories, FOS: Mathematics, Homological functors on modules (Tor, Ext, etc.) in associative algebras, Representations of quivers and partially ordered sets, Category Theory (math.CT), Representation Theory (math.RT), finitistic dimension, Mathematics - Representation Theory
path algebras, Homological dimension in associative algebras, Mathematics - Category Theory, Mathematics - Rings and Algebras, Homological dimension (category-theoretic aspects), recollements of abelian categories, Rings and Algebras (math.RA), Abelian categories, Grothendieck categories, cleft extension of abelian categories, FOS: Mathematics, Homological functors on modules (Tor, Ext, etc.) in associative algebras, Representations of quivers and partially ordered sets, Category Theory (math.CT), Representation Theory (math.RT), finitistic dimension, Mathematics - Representation Theory
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