Related papers: Duality for $K$-analytic Cohomology

We prove a duality theorem for Cohen--Macaulay simplicial complexes. This is a generalisation of Poincar\'e Duality, framed in the language of combinatorial sheaves. Our treatment is self-contained and accessible for readers with a working…

Differentiations of operator algebras over non-archimedean spherically complete fields are investigated. Theorems about a differentiation being internal are demonstrated.

The Weil algebra of a semisimple Lie group and an exterior algebra of a symplectic manifold possess antibrackets. They are applied to formulate the models of non--abelian equivariant cohomologies.

We explicitly compute the Dolbeault cohomologies of certain domains in complex space generalizing the classical Hartogs figure. The cohomology groups are non-Hausdorff topological vector spaces, and it is possible to identify the reduced…

We prove that the $0$-th local cohomology of the jacobian ring of a projective hypersurface with isolated singularities has a nice interpretation it in the context of linkage theory. Roughly speaking, it represents a measure of the failure…

Let $\mathbf{K}$ be an algebraically closed field of arbitrary characteristic, complete with respect to a non-archimedean absolute value $|\,|$. We establish a Second Main Theorem type estimate for analytic map $f\colon…

We invent a new cohomology theory for Lie triple algebras. Using this cohomology, we introduce the notions of 2-term $L_\infty$-triple algebras and Lie triple 2-algebras. We prove that the category of 2-term $L_\infty$-triple algebras is…

For the double complex structure of grading-restricted vertex algebra cohomology defined in \cite{Huang}, we introduce a multiplication of elements of double complex spaces. We show that the orthogonality and bi-grading conditions applied…

We study generalized electric/magnetic duality in Abelian gauge theory by combining techniques from locally covariant quantum field theory and Cheeger-Simons differential cohomology on the category of globally hyperbolic Lorentzian…

We construct proper pushforwards for partially proper morphisms of analytic adic spaces. This generalises the theory due to van der Put in the case of rigid analytic varieties over a non-Archimedean field. For morphisms which are smooth and…

We study representations of hemistrict Lie 2-algebras and give a functorial construction of their cohomology. We prove that both the cohomology of an injective hemistrict Lie 2-algebra $L$ and the cohomology of the semistrict Lie 2-algebra…

This paper investigates cohomology and support varieties for Lie superalgebras and restricted Lie superalgebras over a field of characteristic 2. The existence of an underlying ordinary Lie algebra allows us to obtain results that are still…

In this paper we construct a graded Lie algebra on the space of cochains on a $\mathbbZ_2$-graded vector space that are skew-symmetric in the odd variables. The Lie bracket is obtained from the classical Gerstenhaber bracket by (partial)…

In a previous paper of the author, we establish a duality for the direct limit and the inverse limit of higher even $K$-groups over a $\mathbb{Z}_p^d$-extension. In this paper, we shall establish such a duality over certain non-commutative…

In this paper, we define a new cohomology theory for multiplicative Hom-pre-Lie algebras which controls deformations of Hom-pre-Lie algebra structure. This new cohomology is a natural one by considering the structure map. We develop…

We prove a series of van Est type theorems relating the cohomologies of strict Lie 2-groups and strict Lie 2-algebras and use them to prove the integrability of Lie 2-algebras anew.

Classical contact Lie algebras are the fundamental algebraic structures on the manifolds of contact elements of configuration spaces in classical mechanics. Xu introduced a large category of contact simple Lie algebras which are related to…

We first prove that, for any generalized Hamiltonian type Lie algebra $L$, the first cohomology group $H^1(L,L \otimes L)$ is trivial. We then show that all Lie bialgebra structures on $L$ are triangular.

We obtain formulas for the first and second cohomology groups of a general current Lie algebra with coefficients in the "current" module, and apply them to compute structure functions for manifolds of loops with values in compact Hermitian…

Let $\mathbb{K}$ be a field, $R$ be an associative and commutative $\mathbb{K}$-algebra and $L$ be a Lie algebra over $\mathbb{K}$. We give some descriptions of injections from $L$ to Lie algebra of $\mathbb{K}$-derivations of $R$ in the…