Related papers: Essential dimension of projective orthogonal and s…
In this paper we discuss various aspects of the problem of determining the minimal dimension of an injective linear representation of a finite semigroup over a field. We outline some general techniques and results, and apply them to…
A dimension group is an ordered abelian group that is an inductive limit of a sequence of simplicial groups, and a stationary dimension group is such an inductive limit in which the homomorphism is the same at every stage. If a simple…
The number of nonisomorphic simplicial complexes with up to $n$ vertices increases super-exponentially with $n$, which makes exhaustive computation of invariants associated with such complexes a daunting task. In this paper we provide a…
We investigate strictly developable simple complexes of groups with arbitrary local groups, or equivalently, group actions admitting a strict fundamental domain. We introduce a new method for computing the cohomology of such groups. We also…
We show that the group of proper projective similitudes of a totally decomposable algebra with involution of the first kind over a field of characteristic different from 2 is R-trivial.
We compare the notions of essential dimension and stable cohomological dimension of a finite group G, prove that the latter is bounded by the length of any normal series with cyclic quotients for G, and show that, however, this bound is not…
We produce a short and elementary algorithm to compute an upper bound for the canonical dimension of a spit semisimple linear algebraic group. Using this algorithm we confirm previously known bounds by Karpenko and Devyatov as well as we…
We initiate a study of varieties of minimal degree in weighted projective spaces. We call a weighted projective space $\mathbf{P}(w_0,\dots,w_n)$ divisible if $w_i \mid w_{i+1}$ for all $i$. We provide sharp bounds for when a non-degenerate…
The central extension of a new infinite dimensional algebra which has both $W_\infty$ and affine $sl(2,R)$ as subalgebras is found. The critical dimension of the corresponding string model is $D=5$.
Three new examples of 4-dimensional irreducible symplectic V-manifolds are constructed. Two of them are relative compactified Prymians of a family of genus-3 curves with involution, and the third one is obtained from a Prymian by Mukai's…
We show that the special unitary group associated to an involution of the second kind on a central division algebra of degree three does not contain hermitian or skew-hermitian elements. Especially, there are no reflections. For Albert's…
I. Schur studied double covers $\widetilde{\Sym}^{\pm}_n$ and $\widetilde{\Alt}_n$ of symmetric groups $\Sym_n$ and alternating groups $\Alt_n$, respectively. Representations of these groups are closely related to projective representations…
We construct four families of Artin-Schelter regular algebras of global dimension four. Under some generic conditions, this is a complete list of Artin-Schelter regular algebras of global dimension four that are generated by two elements of…
The theory of algebras with polynomial identities has developed significantly, with special attention devoted to the classification of varieties according to the asymptotic behavior of their codimension sequences. This sequence is a…
We study fundamental groups of projective varieties with normal crossing singularities and of germs of complex singularities. We prove that for every finitely-presented group G there is a complex projective surface S with simple normal…
We give a characterisation of representation-finite symmetric algebras of period four, and describe their basic algebras. In particular, if such an algebra is indecomposable, it has at most two simple modules.
We study the Incipient Infinite Cluster (IIC) of high-dimensional bond percolation on $\mathbb{Z}^d$. We prove that the mass dimension of IIC almost surely equals $4$ and the volume growth exponent of IIC almost surely equals $2$.
Trialitarian triples are triples of central simple algebras of degree 8 with orthogonal involution that provide a convenient structure for the representation of trialitarian algebraic groups as automorphism groups. This paper explicitly…
In this article, we develop a further adaptation of the method of Skjelbred-Sund to construct central extensions of axial algebras. We use our method to prove that all axial central extensions (with respect to a maximal set of axes) of…
We start with definitions of the general notions of the theory of $\Bbb Z_{2}$-graded algebras. Then we consider theory of inductive families of $\Bbb Z_{2}$-graded semisimple finite-dimensional algebras and its representations in the…