Conformal algebras, vertex algebras, and the logic of locality

Rok, strany: 2016, 407 - 420

In a new algebraic approach, conformal algebras and vertex algebras are extended to two-sorted structures, with an additional component encoding the logical properties of locality. Within these algebras, locality is expressed as an identity, without the need for existential quantifiers. Two-sorted conformal algebras form a variety of two-sorted algebras, an equationally-defined class, and free conformal algebras are given by standard universal algebraic constructions. The variety of two-sorted conformal algebras is equivalent to a Mal'tsev variety of single-sorted algebras. Motivated by a question of Griess, subalgebras of reducts of conformal algebras are shown to satisfy a set of quasi-identities. The class of two-sorted vertex algebras does not form a variety, so open problems concerning the nature of that class are posed.

ISO 690:

Smith, J. 2016. Conformal algebras, vertex algebras, and the logic of locality. In Mathematica Slovaca, vol. 66, no.2, pp. 407-420. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0146

APA:

Smith, J. (2016). Conformal algebras, vertex algebras, and the logic of locality. Mathematica Slovaca, 66(2), 407-420. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0146