Related papers: Algebraic properties of some varieties of central …
Isotropic odd unitary groups generalize Chevalley groups of classical types over commutative rings and their twisted forms. Such groups have root subgroups parameterized by a root system $\mathsf{BC}_\ell$ and may be constructed by…
We determine the irreducible representations of alternating and symmetric groups and their universal central extensions that contain a non-scalar element with all but one eigenvalues of multiplicity 1. The ground field is algebraically…
We study non-associative twisted group algebras over $(\Z_2)^n$ with cubic twisting functions. We construct a series of algebras that extend the classical algebra of octonions in the same way as the Clifford algebras extend the algebra of…
A surface S in R^3 has the central plane oval property (cpo) if (i) S meets at least one affine plane transversally along a strictly convex oval, and (ii) Every such transverse oval on S has central symmetry. We show that a complete,…
This paper proves that the variety generated by a centrally nilpotent Moufang loop (or centrally nilpotent A-loop) is finitely based.
Properties of the inverse along an element in rings with an involution, Banach algebras and $C^*$-alegbras will be studied unifying known expressions concerning generalized inverses.
The distributive property can be studied through bilinear maps and various morphisms between these maps. The adjoint-morphisms between bilinear maps establish a complete abelian category with projectives and admits a duality. Thus the…
Given two algebras A and B, sometimes assumed to be C*-algebras, we consider the question of putting algebra or C*-algebra structures on the tensor product A\otimes B. In the C*-case, assuming B to be two-dimensonal, we characterize all…
We obtain several new characterizations of ultrametric spaces in terms of roundness, generalized roundness, strict p-negative type, and p-polygonal equalities (p > 0). This allows new insight into the isometric embedding of ultrametric…
We study structurable algebras and their associated Freudenthal triple systems over commutative rings. The automorphism groups of these triple systems are exceptional groups of type $\mathrm{E}_7$, and we realize groups of type…
We study a variety of loops, RIF, which arise naturally from considering inner mapping groups, and a somewhat larger variety, ARIF. All Steiner and Moufang loops are RIF, and all flexible C-loops are ARIF. We show that all ARIF loops are…
We initiate a systematic study of quantum properties of finite graphs, namely, quantum asymmetry, quantum symmetry, and quantum isomorphism. We define the Schmidt alternative for a class of graphs, which reveals to be a useful tool for…
The volume of a cyclic polytope can be obtained by forming an iterated integral along a suitable piecewise linear path running through its edges. Different choices of such a path are related by the action of a subgroup of the combinatorial…
For an isotropic reductive group G satisfying a suitable rank condition over an infinite field k, we show that the sections of the $\mathbb{A}^1$-fundamental group sheaf of G over an extension field L/k can be identified with the second…
The class of all quasigroups is covered by six classes: the class of all asymmetric quasigroups and five varieties of quasigroups (commutative, left symmetric, right symmetric, semi-symmetric and totally symmetric). Each of these classes is…
Solving functional equations given in \cite{nagy} for extensions of a group $A$ by a weighted Steiner loop $S$ we obtain concrete description for all loops with interesting weak associativity properties if the Steiner loop $S$ induces only…
In this article several properties of the inverse along an element will be studied in the context of unitary rings. New characterizations of the existence of this inverse will be proved. Moreover, the set of all invertible elements along a…
We investigate the Wall form of unipotent elements of index two in the orthogonal group and obtain a decomposition for these elements. Also, in characteristic two, the relation between the Wall form and some invariants of the induced…
In this paper we give a characterisation of real closure * of regular rings, which is quite similar to the characterisation of real closure * of Baer regular rings seen in [4]. We also characterize Baer-ness of regular rings using near-open…
A loop is automorphic if its inner mappings are automorphisms. Using so-called associated operations, we show that every commutative automorphic loop of odd prime power order is centrally nilpotent. Starting with anisotropic planes in the…