Gr\"obner-Shirshov bases for associative conformal modules
Yuqun Chen, Lili Ni
TL;DR
This paper develops a framework for constructing free modules over associative conformal algebras, establishing a Composition-Diamond lemma, and applying these results to specific modules like Virasoro, advancing algebraic methods in conformal algebra theory.
Contribution
It introduces Gr"obner-Shirshov bases for associative conformal modules and applies them to important examples such as Virasoro modules.
Findings
Established Composition-Diamond lemma for associative conformal modules
Constructed Gr"obner-Shirshov bases for Virasoro conformal modules
Provided bases for modules over semidirect products of conformal algebras
Abstract
We construct free modules over an associative conformal algebra. We establish Composition-Diamond lemma for associative conformal modules. As applications, Gr\"obner-Shirshov bases of the Virasoro conformal module and module over the semidirect product of Virasoro conformal algebra and current algebra are given respectively.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons