Related papers: 2-track algebras and the Adams spectral sequence
The spectra of recently constructed auxiliary matrices for the six-vertex model respectively the spin s=1/2 Heisenberg chain at roots of unity q^N=1 are investigated. Two conjectures are formulated both of which are proven for N=3 and are…
We classify, up to isomorphism, the 2-dimensional algebras over a field K. We focuse also on the case of characteristic 2, identifying the matrices of GL(2,F_2) with the elements of the symmetric group S_3. The classification is then given…
We prove a family of 3-term relations in the Grothendieck ring of the category of finite-dimensional modules over the affine quantum algebra of type $G_2$ extending the celebrated $T$-system relations of type $G_2$. We show that these…
Recently designed biomolecular approaches to build single chain polypeptide polyhedra as molecular origami nanostructures have risen high interest in various double traces of the underlying graphs of these polyhedra. Double traces are walks…
Given an extriangulated category $(\mathcal{C},\mathbb{E},\mathfrak{s})$, we introduce the $3 \times 3$-lemma property for subfunctors of $\mathbb{E}$ and prove that an additive subfunctor $\mathbb{F}$ of $\mathbb{E}$ is closed if, and only…
The paper pursues three objectives. Firstly, we provide an expanded version of spectral analysis of self-adjoint Toeplitz operators, initially built by M. Rosenblum in the 1960's. We offer some improvements to Rosenblum's approach: for…
We make use of the cotangent complex formalism developed by Lurie to formulate Quillen cohomology of algebras over an enriched operad. Additionally, we introduce a spectral Hochschild cohomology theory for enriched operads and algebras over…
A classification of the semisimple subalgebras of the Lie algebra of traceless $3\times 3$ matrices with complex entries, denoted $A_2$, is well-known. We classify its nonsemisimple subalgebras, thus completing the classification of the…
In the paper we describe complexes whose homologies are naturally isomorphic to the first term of the Vassiliev spectral sequence computing (co)homology of the spaces of long knots in R^d, d>=3. The first term of the Vassiliev spectral…
The trace or the $0$th Hochschild--Mitchell homology of a linear category $\mathcal{C}$ may be regarded as a kind of decategorification of $\mathcal{C}$. We compute traces of the two versions $\dot{\mathcal{U}}$ and $\dot{\mathcal{U}}^*$ of…
We combine the theory of traces in homotopical algebra with sheaf theory in derived algebraic geometry to deduce general fixed point and character formulas. The formalism of dimension (or Hochschild homology) of a dualizable object in the…
We study the cohomology of certain local systems on moduli spaces of principally polarized abelian surfaces with a level 2 structure. The trace of Frobenius on the alternating sum of the \'etale cohomology groups of these local systems can…
For any additive functor from modules (or, more generally, from an abelian category with enough projectives or injectives), we construct long sequences tying up together the derived functors, the satellites, and the stabilizations of the…
In a previous paper, we obtained a general trace formula for double coset operators acting on modular forms for congruence subgroups, expressed as a sum over conjugacy classes. Here we specialize it to the congruence subgroups $\Gamma_0(N)$…
This is the first in a sequence of articles exploring the relationship between commutative algebras and $E_\infty$-algebras in characteristic $p$ and mixed characteristic. In this paper we lay the groundwork by defining a new class of…
We continue classification of finite groups which can be used as symmetry group of the scalar sector of the four-Higgs-doublet model (4HDM). Our objective is to systematically construct non-abelian groups via the group extension procedure,…
We separate the $AF$-algebras (correspondingly action of the countable groups on Cantor sets) onto two classes ---- "completely smooth" for which the set of all indecomposable traces (correspondingly list of all invariant ergodic measures)…
This paper is an expanded version of the author's lecture at the Integers Conference 2011. We discuss the secondary terms in the Davenport-Heilbronn theorems on cubic fields and 3-torsion in class groups of quadratic fields. Such secondary…
We construct spectral triples and, in particular, Dirac operators, for the algebra of continuous functions on certain compact metric spaces. The triples are countable sums of triples where each summand is based on a curve in the space.…
We show that the hypercohomology of the Chevalley-Eilenberg-de Rham complex of a Lie algebroid L over a scheme with coefficients in an L-module can be expressed as a derived functor. We use this fact to study a Hochschild-Serre type…