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Integrable systems in low dimensions, constructed through the symmetry reduction method, are studied using phase portrait and variable separation techniques. In particular, invariant quantities and explicit periodic solutions are…
We classify irreducible homogeneous almost Hermite-Lorentz spaces of complex dimension 3.
Structures in low-dimensional topology and low-dimensional geometry -- often combined with ideas from (quantum) field theory -- can explain and inspire concepts in algebra and in representation theory and their categorified versions. We…
Finite semisimple group algebras for which all the minimal ideals are easily computable dimension (ECD) are characterized and some lower bounds for the minimum Hamming distance of group codes in these algebras are offered. Examples…
We consider a category whose morphisms are bordisms of $n$-dimensional pseudomanifolds equipped with a certain additional structure (coloring). On the other hand, we consider the product $G$ of $(n+1)$ copies of infinite symmetric group. We…
A classification of (countable) direct limits of finite dimensional involution simple associative algebras over an algebraically closed field of arbitrary characteristic is obtained. This also classifies the corresponding dimension groups.…
In this paper we continue our investigation of the global categorical symmetries that arise when gauging finite higher groups and their higher subgroups with discrete torsion. The motivation is to provide a common perspective on the…
We determine the minimal equivariant embedding dimension of orthgonal groups acting on real flag manifolds and unitary groups acting on complex flag manifolds. The minimal embedding dimension is achieved at isospectral model.
We define basic notions in the category of conic representations of a topological group and prove elementary facts about them. We show that a conic representation determines an ordinary dynamical system of the group together with a…
A unitary representation of a, possibly infinite dimensional, Lie group $G$ is called semibounded if the corresponding operators $i\dd\pi(x)$ from the derived representation are uniformly bounded from above on some non-empty open subset of…
The set of linear, differential operators preserving the vector space of couples of polynomials of degrees n and n-2 in one real variable leads to an abstract associative graded algebra A(2). The irreducible, finite dimensional…
We classify nilpotent associative algebras of dimensions up to 4 over any field. This is done by constructing the nilpotent associative algebras as central extensions of algebras of smaller dimension, analogous to methods known for…
We find a one-to-one correspondence between full extrinsic symmetric spaces in (possibly degenerate) inner product spaces and certain algebraic objects called (weak) extrinsic symmetric triples. In particular, this yields a description of…
We study the complex irreducible representations of special linear, symplectic, orthogonal and unitary groups over principal ideal local rings of length two. We construct a canonical correspondence between the irreducible representations of…
In this paper we study certain category of smooth modules for reductive $p$--adic groups analogous to the usual smooth complex representations but with the field of complex numbers replaced by a $\mathbb Q$--algebra. We prove some…
The article is devoted to some ``strange'' phenomena of representation theory and their interrelations. Cross-projective representations of pairs of anticommutative algebras, alloys, their universal envelopping Lie algebras and their…
We investigate the representations and the structure of Hecke algebras associated to certain finite complex reflection groups. We first describe computational methods for the construction of irreducible representations of these algebras,…
We extend a classification of irreducible, almost commutative geometries whose spectral action is dynamically non-degenerate to internal algebras that have four simple summands.
Using irreducible representations of semi simple Lie algebras, we construct Klein geometries of arbitrarily high order.
We consider quotients of the group algebra of the $3$-string braid group $B_3$ by $p$-th order generic polynomial relations on the elementary braids. In cases $p=2,3,4,5$ these quotient algebras are finite dimensional. We give…