Related papers: On the lambda algebra and Singer's cohomological t…
We study algebras k[x_1,...,x_n]/I which admit a grading by a subsemigroup of N^d such that every graded component is a one-dimensional k-vector space. V.I.~Arnold and coworkers proved that for d = 1 and n <= 3 there are only finitely many…
The aim of this work is to generalize Johnson's techniques in order to apply them to establish a bijective correspondence between $S$-derivations and continuous derivations on $M_a(S,\omega),$ where $S$ is a locally compact foundation…
We study algebra endomorphisms and derivations of some localized down-up algebras $\A$. First, we determine all the algebra endomorphisms of $\A$ under some conditions on $r$ and $s$. We show that each algebra endomorphism of $\A$ is an…
Let $\lambda$ be a primitive root of unity of order $\ell$. We introduce a family of finite-dimensional algebras $\{\mathcal{D}_{\lambda,N}(\mathfrak{sl}_2)\}_{N\in\mathbb{N}_0}$ over the complex numbers, such that…
We characterize isometric actions whose principal orbits are hypersurfaces through the existence of a linear connection satisfying a set of covariant equations in the same spirit as the Ambrose-Singer Theorem for homogeneous space. These…
The main goal of this paper is to compare the silting theory of an $R$-algebra $\Lambda$ over a Noetherian ring $R$ with that of its tensor product $\Lambda \otimes \Gamma$ with another $R$-algebra $\Gamma$. In the case that the $R$-algebra…
The main result of this article provides a characterization of reductive homogeneous spaces equipped with some geometric structure (non necessarily pseudo-Riemannian) in terms of the existence of certain connection. The result generalizes…
These expository notes are dedicated to the study of the topology of configuration spaces of manifolds. We give detailed computations of many invariants, including the fundamental group of the configuration spaces of $\mathbb{R}^2$, the…
In the realm of invertible symmetry, the topological approach based on classifying spaces dominates the classification of 't Hooft anomalies and symmetry protected topological phases. We explore the alternative algebraic approach based on…
In Homotopy Type Theory, cohomology theories are studied synthetically using higher inductive types and univalence. This paper extends previous developments by providing the first fully mechanized definition of cohomology rings. These rings…
Scheme-theoretic methods are used to classify ternary quadratic forms with values in line bundles over arbitrary schemes and to canonically determine the isomorphisms between them. The association of a quadratic bundle to its even Clifford…
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…
Cohomology of a topological space with coefficients in stacks of abelian 2-groups is considered. A 2-categorical analog of the theorem of Grothendieck is proved, relating cohomology of the space with coefficients in a 2-stage spectrum and…
Given a simply connected space $X$ with the cohomology $H^*(X;{\mathbb Z}_2)$ to be polynomial, we calculate the loop cohomology algebra $H^*(\Omega X;{\mathbb Z}_2)$ by means of the action of the Steenrod cohomology operation $Sq_1$ on…
E. Opdam introduced the tool of spectral transfer morphism (STM) of affine Hecke algebras to study the formal degrees of unipotent discrete series representations. He established a uniqueness property of STM for the affine Hecke algebras…
For a braided vector space $(V,\sigma)$ with braiding $\sigma$ of Hecke type, we introduce three associative algebra structures on the space $\oplus_{p=0}^{M}\mathrm{End}S_\sigma^p(V)$ of graded endomorphisms of the quantum symmetric…
Continuing work begin in arXiv:1910.12609, we interpret the Hurewicz homomorphism for Baker and Richter's noncommutative complex cobordism spectrum $M\xi$ in terms of characteristic numbers (indexed by quasi-symmetric functions) for…
In previous work we introduced the notion of binomial cup-one algebras, which are differential graded algebras endowed with Steenrod $\cup_1$-products and compatible binomial operations. In this paper we show that binomial cup-one algebras…
We prove that within a natural class of E_3-algebras, the graded Tor group induced by a span of E_3-algebra maps carries a graded algebra structure generalizing the classical structure when the algebras are genuine commutative differential…
Soergel bimodules and their Hochschild homology are known to be important in the context of link homology. In this article we observe that Soergel bimodules may be naturally identified as the cohomology of well-defined objects in the…