Reference : Multi-oriented props and homotopy algebras with branes
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Multi-oriented props and homotopy algebras with branes
Merkulov, Sergei mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Letters in Mathematical Physics
Kluwer Academic Publishers
Yes (verified by ORBilu)
[en] algebra, operad, homotopy theory
[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.

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