相关论文: The Lambda algebra and Sq_0

A method of classification of integrable equations on quad-graphs is discussed based on algebraic ideas. We assign a Lie ring to the equation and study the function describing the dimensions of linear spaces spanned by multiple commutators…

We explicitly compute examples of sheaves over the projectivization of the spectrum of the cohomology of sl_2. In particular, we compute \ker\Theta_M for every indecomposable M and we compute F_i(M) when M is an indecomposable Weyl module…

Let $\Lambda$ be a Legendrian in the jet space of some manifold $X$. To a generating family presentation of $\Lambda$, we associate a constructible sheaf on $X \times \mathbb{R}$ whose singular support at infinity is $\Lambda$, and such…

The quantum group SL_q(2,R) at roots of unity is introduced by means of duality pairings with the quantum algebra U_q(sl(2,R)). Its irreducible representations are constructed through the universal T-matrix. An invariant integral on this…

We show how to induce products in sheaf cohomology for a wide variety of coefficients: sheaves of dg commutative and Lie algebras, symmetric Omega-spectra, filtered dg algebras, operads and operad algebras.

A dendriform algebra is an associative algebra whose product splits into two binary operations and the associativity splits into three new identities. These algebras arise naturally from some combinatorial objects and through Rota-Baxter…

A stable homology theory is defined for completely distributive CSL algebras in terms of the point-neighbourhood homology of the partially ordered set of meet-irreducible elements of the invariant projection lattice. This specialises to the…

We propose a skein model for the quantum cluster algebras of surface type with coefficients. We introduce a skein algebra $\mathscr{S}_{\Sigma,\mathbb{W}}^{A}$ of a walled surface $(\Sigma,\mathbb{W})$, and prove that it has a quantum…

It is demonstrated that decompositions of integrable highest weight modules of a simple Lie algebra with respect to its reductive subalgebra obey the set of algebraic relations leading to the recursive properties for the corresponding…

Lando framed graph bialgebra is generated by framed graphs modulo 4-term relations. We provide an explicit set of generators of its primitive subspace and a description of the set of relations between the generators. We also define an…

We describe an algorithm that allows to compute a minimal resolution of the Steenrod algebra. The algorithm has built-in knowledge about vanishing lines for the cohomology of sub Hopf algebras of the Steenrod algebra which makes it both…

Let Gamma be a congruence subgroup of the Picard modular group of an imaginary number field k, and let D be the associated symmetric space. We describe a method to compute the integral cohomology of the locally symmetric space Gamma\D. The…

We study the behaviors of cohomological Hall algebras and relevant subjects under an edge contraction. Given a quiver with potential and fix an arrow, the edge contraction is a way to construct a new quiver with potential. We show that…

Deformation theory can be used to compute the cohomology of a deformed algebra with coefficients in itself from that of the original. Using the invariance of the Euler-Poincare characteristic under deformation, it is applied here to compute…

In this paper, first we construct a Lie 2-algebra associated to every Leibniz algebra via the skew-symmetrization. Furthermore, we introduce the notion of the naive representation for a Leibniz algebra in order to realize the abstract…

We describe the variety of `symmetric' left actions of the mod 2 Steenrod algebra $\mathcal{A}$ on its subalgebra $\mathcal{A}(2)$. These arise as the cohomology of $\text{v}_2$ self maps $\Sigma^7 Z \longrightarrow Z$, as in…

Let $K$ denote a field with characteristic 0 and let $T$ denote an indeterminate. We give a presentation for the three-point loop algebra $\mathfrak{sl}_2 \otimes K\lbrack T, T^{-1},(T-1)^{-1}\rbrack$ via generators and relations. This…

The ${\rm SL}_n$-skein algebra of a punctured surface $\mathfrak{S}$, studied by Sikora, is an algebra generated by isotopy classes of $n$-webs living in the thickened surface $\mathfrak{S} \times (-1,1)$, where an $n$-web is a union of…

Let $N>1$ be an integer, and let $\Gamma = \Gamma_0 (N) \subset \SL_4 (\Z)$ be the subgroup of matrices with bottom row congruent to $(0,0,0,*)\mod N$. We compute $H^5 (\Gamma; \C) $ for a range of $N$, and compute the action of some Hecke…

We investigate the relationship between endomorphisms of the Cuntz algebra ${\mathcal O}_2$ and endomorphisms of the Thompson groups $F$, $T$ and $V$ represented inside the unitary group of ${\mathcal O}_2$. For an endomorphism $\lambda_u$…