Odd Structures Are Odd

0474671 - MÚ 2018 RIV CH eng J - Journal Article
Markl, Martin
Odd Structures Are Odd.
Advances in Applied Clifford Algebras. Roč. 27, č. 2 (2017), s. 1567-1580. ISSN 0188-7009. E-ISSN 1661-4909
Institutional support: RVO:67985840
Keywords : graded vector space * monoidal structure * Odd endomorphism operad
OECD category: Pure mathematics
Impact factor: 1.174, year: 2017
http://link.springer.com/article/10.1007%2Fs00006-016-0720-8

By an odd structure we mean an algebraic structure in the category of graded vector spaces whose structure operations have odd degrees. Particularly important are odd modular operads which appear as Feynman transforms of modular operads and, as such, describe some structures of string field theory. We will explain how odd structures are affected by the choice of the monoidal structure of the underlying category. We will then present two ‘natural’ and ‘canonical’ constructions of an odd modular endomorphism operad leading to different results, only one being correct. This contradicts the generally accepted belief that the systematic use of the Koszul sign rule leads to correct signs.
Permanent Link: http://hdl.handle.net/11104/0271670