Functional equations in algebra
Boris Feigin, Alexander Odesskii
TL;DR
This paper investigates flat deformations of certain graded commutative algebras using functional equations and theta functions, also exploring a fermionic analog.
Contribution
It introduces a new approach to studying algebra deformations via functional equations and extends the theory to fermionic cases.
Findings
Functional equations are key to understanding algebra deformations.
Solutions involve theta functions, linking algebra and complex analysis.
A brief discussion on fermionic analogs broadens the scope.
Abstract
We study flat deformations of quotients of a polynomial algebra in a class of graded commutative associative algebras. Functional equations and their solutions in terms of theta functions play important role in these studies. An analog of this theory in a fermionic case is also briefly discussed.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons