Fukaya Type Categories for Associative Algebras
Ryszard Nest (University of Copenhagen), Boris Tsygan (Penn State, University)
TL;DR
This paper introduces a new $A_{}$ category for associative algebras, where objects are automorphisms, drawing parallels with Fukaya categories in Floer cohomology.
Contribution
It defines a novel $A_{}$ category for associative algebras based on automorphisms, inspired by Fukaya categories.
Findings
Establishes a new categorical framework for associative algebras.
Draws conceptual parallels with Fukaya categories in symplectic geometry.
Provides foundational definitions for future research in algebraic and geometric contexts.
Abstract
We define for an associative algebra an category whose objects are automorphisms of this algebra. This construction has some resemblance with Fukaya'a categories related to Floer cohomology.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra