We state a conjecture that relates the derived category of smooth representations $p$ -adic split reductive group with (quasi-)coherent sheaves on stack L-parameters. investigate in case principal block ${\rm GL}_n$ by showing functor should be given tensor product family interpolating modified Langlands correspondence over L-parameters is suggested work Helm and Emerton Helm.

Associated to each elliptic root system, we introduce a Lie algebra as an amalgamation of an a ne Kac-Moody algebra and a generalization of a Heisenberg algebra. The derived algebra of the amalgamation algebra is shown to be the universal central extension of a certain twisted loop algebra of two variables.

‎from hilbert's theorem of zeroes‎, ‎and from noether's ideal theory‎, ‎birkhoff derived certain algebraic concepts (as explained by tholen) that have a dual significance in general toposes‎, ‎similar to their role in the original examples of algebraic geometry‎. ‎i will describe a simple example that illustrates some of the aspects of this relationship‎. the dualization from algebra ...

Abstrac t -The relational model is extended to include nested structures. This extension is formalised using the distinction between a tuple scheme and a relation scheme. The algebra and calculus languages are defined for this model. It is shown that the restricted powerset is a derived operation in the algebra and the full powerset is expressible by a safe forraula in the calculus. Since the f...

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We determine the derived representation type of Nakayama algebras and prove that a tame algebra without simple projective module is gentle or equivalent to some skewed-gentle algebra, as consequence, we its singularity category.

Abstract Consider a monoidal category that is at the same time abelian with enough projectives and such are flat on right. We show there $B_{\infty }$-algebra $A_{\infty }$-quasi-isomorphic to derived endomorphism algebra of tensor unit. This obtained as co-Hochschild complex projective resolution unit, endowed lifted }$-coalgebra structure. in classical situation bimodules over an algebra, thi...

The first-order formulation of the principal sigma model with a Lie group target space is performed. By using the dualisation of the algebra and the field content of the theory the field equations which are solely written in terms of the field strengths are realized through an extended symmetry algebra parametrization. The structure of this symmetry algebra is derived so that it generates the r...

In this paper, we review deformation, cohomology and homotopy theories of relative Rota–Baxter ( RB $\mathsf {RB}$ ) Lie algebras, which have attracted quite much interest recently. Using Voronov's higher derived brackets, one can obtain an L ∞ $L_\infty$ -algebra whose Maurer–Cartan elements are algebras. Then using the twisting method, that controls deformations a algebra. Meanwhile, cohomolo...