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 | |
| 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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