相关论文: The n-homology of representations
In this paper we describe a model based on persistent homology that describes interactions between mathematicians in terms of collaborations. Some ideas from classical data analysis are used.
The goal of the memoir is to develop a new cohomology theory which encompasses De Rham and Dolbeault cohomology as well as Deligne Beilinson cohomology, in the context of general complex analytic manifolds. The special case of the Iwasawa…
We introduce the \verb|Macaulay2| package \verb|RepHomology| for the computations of representation homology of certain spaces. The main methods implement computing the representation homology of surfaces (with group coefficients, and…
In this paper, we study gyro-groups associated to groups, group extensions admitting gyro-sections, and corresponding co-homologies. We also describe the obstructions in terms of co-homomology. The notion of gyro-Schur Multiplier and that…
Let G be a reductive algebraic group over a field of prime characteristic. One can associate to G (or subgroups thereof) its Lie algebra, its Frobenius kernels, and the finite Chevalley group of points over a finite field. The…
The first author proved in a previous paper that the n-fold bar construction for commutative algebras can be generalized to E_n-algebras, and that one can calculate E_n-homology with trivial coefficients via this iterated bar construction.…
Let PConf^n M be the configuration space of ordered n-tuples of distinct points on a smooth manifold M admitting a nowhere-vanishing vector field. We show that the ith cohomology group with coefficients in a field H^i(PConf^n M, k) is an…
We give a brief introduction to (upper) cluster algebras and their quantization using examples. Then we present several important families of bases for these algebras using topological models. We also discuss tropical properties of these…
We construct examples of nonresolvable generalized $n$-manifolds, $n\geq 6$, with arbitrary resolution obstruction, homotopy equivalent to any simply connected, closed $n$-manifold. We further investigate the structure of generalized…
In the 40s, Mayer introduced a construction of (simplicial) $p$-complex by using the unsigned boundary map and taking coefficients of chains modulo $p$. We look at such a $p$-complex associated to an $(n-1)$-simplex; in which case, this is…
A multiplication on the 2D cohomological Hall algebra (CoHA) of the variety of commuting matrices was described by Schiffman and Vasserot. This construction can be generalised to other varieties that exist as the zero-locus of a function on…
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…
Aguiar and Mahajan introduced a cohomology theory for the twisted coalgebras of Joyal, with particular interest in the computation of their second cohomology group, which gives rise to their deformations. We use the Koszul duality theory…
This historical introduction is in two parts. The first is reprinted with permission from ``A century of mathematics in America, Part II,'' Hist. Math., 2, Amer. Math. Soc., 1989, pp.543-585. Virtually no change has been made to the…
In this paper we define and discuss the representations of $n$-BiHom-Lie algebra. We also introduce $T_{\theta}$-extensions and $T_{\theta}^{\ast}$-extensions of $n$-BiHom-Lie algebras and prove the necessary and sufficient conditions for a…
We compute numerically the homology of several graph complexes in low loop orders, extending previous results.
The groups of units $U^i_L$ of a local field $L$ play an important role in algebraic number theory, especially in class field theoretic topics. Therefore, it is interesting to study these groups from a cohomological point of view. In this…
This paper is a natural continuation of the previous paper J.Phys. A: Math.Theor. 44 (2011) 425204, arXiv 0907.1736 [quant-ph] where oscillator representations for nonnegative Calogero Hamiltonians with coupling constant $\alpha\geq-1/4$…
The tools and arguments developed by Kevin Costello are adapted to families of "Outer Spaces" or spaces of graphs. This allows us to prove a version of Deligne's conjecture: the Harrison homology associated to a homotopy commutative algebra…
Let $(L, \alpha)$ be a Hom-Lie-Yamaguti superalgebra. We first introduce the representation and cohomology theory of Hom-Lie-Yamaguti superalgebras. Furthermore, we introduce the notions of generalized derivations and representations of…