Quadratic algebras arising from Hopf operads generated by a single element

Anton Khoroshkin

doi:10.1007/s11005-020-01283-z

Quadratic algebras arising from Hopf operads generated by a single element

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Abstract

The operads of Poisson and Gerstenhaber algebras are generated by a single binary element if we consider them as Hopf operads (i.e. as operads in the category of cocommutative coalgebras). In this note we discuss in detail Hopf operads generated by a single skew-symmetric element of arbitrary arity. We explain why the dual space to the space of n-ary operations in these operads are quadratic and Koszul algebras. We give a detailed description of generators, relations and monomial bases in these algebras.

Original language	English
Pages (from-to)	2053-2082
Number of pages	30
Journal	Letters in Mathematical Physics
Volume	110
Issue number	8
DOIs	https://doi.org/10.1007/s11005-020-01283-z
State	Published - 1 Aug 2020
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2020, Springer Nature B.V.

Keywords

Hopf operads
Orlik–Solomon algebra
Quadratic algebras

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s11005-020-01283-z

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Quadratic algebras arising from Hopf operads generated by a single element

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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