Reference : Multi-oriented props and homotopy algebras with branes
 Document type : Scientific journals : Article Discipline(s) : Physical, chemical, mathematical & earth Sciences : Mathematics To cite this reference: http://hdl.handle.net/10993/33801
 Title : Multi-oriented props and homotopy algebras with branes Language : English Author, co-author : Merkulov, Sergei [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] Publication date : Mar-2020 Journal title : Letters in Mathematical Physics Publisher : Kluwer Academic Publishers Volume : 110 Pages : 1425-1475 Peer reviewed : Yes (verified by ORBilu) Audience : International ISSN : 0377-9017 e-ISSN : 1573-0530 City : Dordrecht Country : Netherlands Keywords : [en] algebra, operad, homotopy theory Abstract : [en] We introduce a new category of differential graded {\em multi-oriented}\, props whose representations (called homotopy algebras with branes) in a graded vector space require a choice of a collection of $k$ linear subspaces in that space, $k$ being the number of extra directions (if $k=0$ this structure recovers an ordinary prop); symplectic vector spaces equipped with $k$ Lagrangian subspaces play a distinguished role in this theory. Manin triples is a classical example of an algebraic structure (concretely, a Lie bialgebra structure) given in terms of a vector space and its subspace; in the context of this paper Manin triples are precisely symplectic Lagrangian representations of the {\em 2-oriented} generalization of the classical operad of Lie algebras. In a sense, the theory of multi-oriented props provides us with a far reaching strong homotopy generalization of Manin triples type constructions. Target : Researchers Permalink : http://hdl.handle.net/10993/33801

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