We consider the space of linear maps from a coassociative coalgebra C into a Lie algebra L. Unless C has a cocommutative coproduct, the usual symmetry properties of the induced bracket on Hom(C,L) fail to hold. We define the concept of twisted domain (TD) algebras in order to recover the symmetries and also construct a modified ChevalleyEilenberg complex in order to define the cohomology of suc...

In this paper we construct an L∞ structure on polyvector fields on a vector space V over C where V may be infinite-dimensional. We prove that the constructed L∞ algebra of polyvector fields is L∞ equivalent to the Hochschild complex of polynomial functions on V , even in the infinite-dimensional case. For a finite-dimensional space V , our L∞ algebra is equivalent to the classical Schouten-Nije...

In this paper, we compute the Hecke action of a certain test function on space an unramified principal series connected reductive group over non-archimedean local field. The key our computation is theory Iwahori–Hecke algebra. As application, obtain new expression L-functions representations.

A new notion of SP-compactness is introduced in L-topological spaces by means of semi-preopen L-sets and their inequality, where L is a complete De Morgan algebra. This new notion does not depend on the structure of basis lattice L and L does not require any distributivity. This new notion implies semicompactness, hence it also implies compactness. This new notion is a good extension and it has...

The L∞-algebra controlling simultaneous deformations of a morphism of associative algebras and its domain and codomain is described. Isomorphism of the cohomology of this L∞-algebra with the classical construction is shown.