Deformation Expression for Elements of Algebra
H.Omori, Y.Maeda, N.Miyazaki, A.Yoshioka
TL;DR
This paper introduces a new concept of deforming the expressions of algebraic elements, extending the idea of deformation quantization from algebraic structures to their expression forms.
Contribution
It proposes a novel notion of deformation for the expressions of algebra elements, broadening the scope of deformation quantization beyond algebraic structures.
Findings
Defines deformation of expressions for algebra elements
Connects deformation of expressions to deformation quantization
Provides a framework for non-commutative expression deformation
Abstract
The purpose of this paper is to give a notion of deformation of expressions for elements of algebra. Deformation quantization (cf.[BF]) deforms the commutative world to a non-commutative world. However, this involves deformation of expression of elements of algebras even from a commutative world to another commutative world. This is indeed a deformation of expressions for elements of algebra.
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Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models