Related papers: Cohomology of truncated polynomial lambda-rings
Braided algebras are associative algebras endowed with a Yang-Baxter operator that satisfies certain compatibility conditions involving the multiplication. Along with Hochschild cohomology of algebras, there is also a notion of Yang-Baxter…
The purpose of this paper is to study Lie-Rinehart superalgebras over characteristic zero fields, which are consisting of a supercommutative associative superalgebra $A$ and a Lie superalgebra $L$ that are compatible in a certain way. We…
The quotient cohomology of tiling spaces is a topological invariant that relates a tiling space to one of its factors, viewed as topological dynamical systems. In particular, it is a relative version of the tiling cohomology that…
Given the L-series of a half-integral weight cusp form, we construct a cohomology class with coefficients in a finite dimensional vector space in a way that parallels the Eichler cohomology in the integral weight case. We also define a lift…
The cotangent cohomology groups T^1 and T^2 play an important role in deformation theory, the first as space of infinitesimal deformations, while the obstructions land in the second. Much work has been done to compute their dimension for…
Inspired by Bhatt-Morrow-Scholze's work on ${\rm THH}$, we define Nygaard-completed log prismatic cohomology based on log topological Hochschild homology via filtrations on log ${\rm THH}$ and its variants. Moreover, of independent…
We derive basic properties of minimal extensions of local rings and their restrictions to subrings. Some applications are included to subrings of truncated polynomial rings.
We define a relative version of tiling cohomology for the purpose of comparing the topology of tiling spaces when one is a factor of the other. We illustrate this with examples, and outline a method for computing the cohomology of tiling…
The space $\Gamma_X$ of all locally finite configurations in a Riemannian manifold $X$ of infinite volume is considered. The deRham complex of square-integrable differential forms over $\Gamma_X$, equipped with the Poisson measure, and the…
Any hodge integrals involving psi-classes and one lambda-class is computed as a polynomial in terms of lower-dimensional ones. Algorithm and examples are presented.
This is a detailed introductory survey of the cohomological dimension theory of compact metric spaces.
Homology has long been accepted as an important computable tool for quantifying complex structures. In many applications, these structures arise as nodal domains of real-valued functions and are therefore amenable only to a numerical study…
We explore and extend the application of homological algebra to describe quantum entanglement, initiated in arXiv:1901.02011, focusing on the Hodge-theoretic structure of entanglement cohomology in finite-dimensional quantum systems. We…
Consistent nontrivial interactions within a special class of covariant mixed-symmetry type tensor gauge fields of degree three are constructed from the deformation of the solution to the master equation combined with specific cohomological…
In this paper, we study Hom-Lie superalgebras of Heisenberg type. For 3-dimensional Heisenberg Hom-Lie superalgebras, we describe their Hom-Lie super structures, compute the cohomology spaces and characterize their infinitesimal…
We compute the quantum cohomology relative to a Lagrangian submanifold in some complete intersections. For quadric hypersurfaces, we also give a full computation of the genus zero open Gromov-Witten invariants.
We study formal deformations of multiplication in an operad. This closely resembles Gerstenhaber's deformation theory for associative algebras. However, this applies to various algebras of Loday-type and their twisted analogs. We explicitly…
In this paper, the discriminant of homogeneous polynomials is studied in two particular cases: a single homogeneous polynomial and a collection of n-1 homogeneous polynomials in n variables. In these two cases, the discriminant is defined…
We prove the existence of two long exact sequences relating the Hochschild cohomology of a triangular matrix algebra with the Hochschild homology of its component subalgebras. We also study the structure of the maps of the first sequence.
In this paper, we define representations and cohomology of weighted Rota-Baxter Lie algebras. As applications of cohomology, we study abelian extensions and formal $1$-parameter deformations weighted Rota-Baxter Lie algebras. Finally, we…