Related papers: Cocharacters of generalized polynomial identities
In this paper, the second of a series of two, we continue the study of higher index theory for expanders. We prove that if a sequence of graphs has girth tending to infinity, then the maximal coarse Baum-Connes assembly map is an…
Let $\mathfrak{L}$ be a Leibniz algebra, $E$ a vector space and $\pi : E \to \mathfrak{L}$ an epimorphism of vector spaces with $ \mathfrak{g} = {\rm Ker} (\pi)$. The global extension problem asks for the classification of all Leibniz…
Extensivity of a category may be described as a property of coproducts in the category, namely, that they are disjoint and universal. An alternative viewpoint is that it is a property of morphisms in a category. This paper explores this…
Complement-reducible graphs (or cographs) are the graphs formed from the single-vertex graph by the operations of complement and disjoint union. By combining the Johnson-Newman theorem on generalized cospectrality with the standard tools in…
We construct self-adjoint operators in the direct sum of a complex Hilbert space $H$ and a finite dimensional complex inner product space $W$. The operator theory developed in this paper for the Hilbert space $H\oplus W$ is originally…
We show in this paper that every domain in a separable Hilbert space, say $\cH$, which has a $C^2$ smooth strongly pseudoconvex boundary point at which an automorphism orbit accumulates is biholomorphic to the unit ball of $\cH$. This is…
We describe a bigraded cocommutative Hopf algebra structure on the weight zero compactly supported rational cohomology of the moduli space of principally polarized abelian varieties. By relating the primitives for the coproduct to graph…
The interpretation of the Meixner-Pollaczek, Meixner and Laguerre polynomials as overlap coefficients in the positive discrete series representations of the Lie algebra su(1,1) and the Clebsch-Gordan decomposition leads to generalisations…
Wawamoto generalized the Witt algebra using Laurent extension of polynomial ring. We construct the generalized Witt algebra $W(g_p,n)$ by using an additive map $g_p$ from a set of integers into a field of characteristic zero where $1\leq p…
We study the cohomology (cocycles) of Lie superalgebras for the generalised complex of forms: superforms, pseudoforms and integral forms. We argue that these cocycles might be interpreted in the light of a new brane scan as generators of…
For the root system of type $A$ we introduce and study a certain extension of the quadratic algebra invented by S. Fomin and the first author, to construct a model for the equivariant cohomology ring of the corresponding flag variety. As an…
We construct a representation of each finitely aligned aperiodic k-graph \Lambda\ on the Hilbert space H^{ap} with basis indexed by aperiodic boundary paths in \Lambda. We show that the canonical expectation on B(H^{ap}) restricts to an…
Two distinct projections of finite rank $m$ are adjacent if their difference is an operator of rank two or, equivalently, the intersection of their images is $(m-1)$-dimensional. We extend this adjacency relation on other conjugacy classes…
It was recently shown that gl^(1|1) admits an infinite family of simple current extensions. Here, these findings are reviewed and explicit free field realisations of the extended algebras are constructed. The leading contributions to the…
Let F be characteristic zero field, G a residually finite group and W a G-prime and PI F-algebra. By constructing G-graded central polynomials for W, we prove the G-graded version of Posner's theorem. More precisely, if S denotes all…
In a Coxeter group $W$, an element is fully commutative if any two of its reduced expressions can be linked by a series of commutation of adjacent letters. These elements have particularly nice combinatorial properties, and also index a…
To each skew-gentle algebra, one can assign a gentle algebra in terms of combinatorial data. In order to relate the structures of the two algebras, we establish a homological epimorphism and a recollement of derived module categories. This…
$W$-algebras are certain algebraic structures associated to a finite dimensional Lie algebra $\mathfrak g$ and a nilpotent element $f$ via Hamiltonian reduction. In this note we give a review of a recent approach to the study of (classical…
Character groups of Hopf algebras appear in a variety of mathematical contexts such as non-commutative geometry, renormalisation of quantum field theory, numerical analysis and the theory of regularity structures for stochastic partial…
We describe a generalization of Hashimoto and Kurano's Cauchy filtration for divided powers algebras. This filtration is then used to provide a cellular structure for generalized Schur algebras associated to an arbitrary cellular algebra.…