arXiv subjects
Publications and source records attributed to Dušan Pagon.
We study polynomial identities of finite dimensional simple color Lie superalgebras over an algebraically closed field of characteristic zero graded by the product of two cyclic groups of order $2$. We prove that the codimensions of identities grow exponentially and the rate of exponent equals the dimension of the algebra. A similar result is also obtained for graded identities and graded codimensions.
We study gradings by noncommutative groups on finite dimensional Lie algebras over an algebraically closed field of characteristic zero. It is shown that if $L$ is gradeg by a non-abelian finite group $G$ then the solvable radical $R$ of $L$ is $G$-graded and there exists a Levi subalgebra $B=H_1\oplus\cdots\oplus H_m$ homogeneous in $G$-grading with graded simple summands $H_1, \ldots, H_m$. All supports $Supp~H_i, i=1\ldots, m$, are commutative subsets of $G$.
In the paper we study inverse semigroups $\mathscr{B}(G)$, $\mathscr{B}^+(G)$, $\bar{\mathscr{B}}(G)$ and $\bar{\mathscr{B}}\,^+(G)$ which are generated by partial monotone injective translations of a positive cone of a linearly ordered group $G$. We describe Green's relations on the semigroups $\mathscr{B}(G)$, $\mathscr{B}^+(G)$, $\bar{\mathscr{B}}(G)$ and $\bar{\mathscr{B}}\,^+(G)$, their bands and show that they are simple, and moreover the semigroups $\mathscr{B}(G)$ and $\mathscr{B}^+(G)$ are bisimple. We show that for a commutative linearly ordered group $G$ all non-trivial congruences on the semigroup $\mathscr{B}(G)$ (and $\mathscr{B}^+(G)$) are group congruences if and only if the group $G$ is archimedean. Also we describe the structure of group congruences on the semigroups $\mathscr{B}(G)$, $\mathscr{B}^+(G)$, $\bar{\mathscr{B}}(G)$ and $\bar{\mathscr{B}}\,^+(G)$.
In this paper we search for conditions on a countably compact (pseudo-compact) topological semigroup under which: (i) each maximal subgroup $H(e)$ in $S$ is a (closed) topological subgroup in $S$; (ii) the Clifford part $H(S)$(i.e. the union of all maximal subgroups) of the semigroup $S$ is a closed subset in $S$; (iii) the inversion $\operatorname{inv}\colon H(S)\to H(S)$ is continuous; and (iv) the projection $π\colon H(S)\to E(S)$, $π\colon x\longmapsto xx^{-1}$, onto the subset of idempotents $E(S)$ of $S$, is continuous.
We study chains in an $H$-closed topological partially ordered space. We give sufficient conditions for a maximal chain $L$ in an $H$-closed topological partially ordered space such that $L$ contains a maximal (minimal) element. Also we give sufficient conditions for a linearly ordered topological partially ordered space to be $H$-closed. We prove that any $H$-closed topological semilattice contains a zero. We show that a linearly ordered $H$-closed topological semilattice is an $H$-closed topological pospace and show that in the general case this is not true. We construct an example an $H$-closed topological pospace with a non-$H$-closed maximal chain and give sufficient conditions that a maximal chain of an $H$-closed topological pospace is an $H$-closed topological pospace.