Differential envelopes of Novikov conformal algebras
P.S. Kolesnikov, A.A. Nesterenko
TL;DR
This paper studies Novikov conformal algebras, showing that finitely generated cases can be embedded into commutative conformal differential algebras, while highlighting limitations for infinitely generated cases.
Contribution
It proves embedding results for finitely generated Novikov conformal algebras into commutative conformal differential algebras.
Findings
Finitely generated Novikov conformal algebras can be embedded into commutative conformal differential algebras.
Embedding does not hold for infinitely generated Novikov conformal algebras.
Every finitely generated Novikov conformal algebra has a differential envelope.
Abstract
A Novikov conformal algebra is a conformal algebra such that its coefficient algebra is right-symmetric and left commutative (i.e., it is an ``ordinary'' Novikov algebra). We prove that every Novikov conformal algebra with a uniformly bounded locality function on a set of generators can be embedded into a commutative conformal algebra with a derivation. In particular, every finitely generated Novikov conformal algebra has a commutative conformal differential envelope. For infinitely generated algebras this statement is not true in general.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Nonlinear Waves and Solitons