Advances in Applied Clifford Algebras

, Volume 27, Issue 2, pp 1567–1580 | Cite as

Odd Structures Are Odd

  • Martin MarklEmail author


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.


Graded vector space Monoidal structure Odd endomorphism operad 

Mathematics Subject Classification

Primary 18D50 Secondary 18D20 18D10 


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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Mathematical Institute of the AcademyPrague 1Czech Republic
  2. 2.Faculty of Mathematics and PhysicsCharles UniversityPrague 8Czech Republic

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