Westudy some structural properties for tree-decompositions of 2-connected planar graphs that we use to improve upon the runtime of tree-decomposition based dynamic programming approaches for several NP-hard planar graph problems. E.g., we derive the fastest algorithm for Planar Dominating Set of runtime 3tw · nO(1), when we take the width tw of a given tree-decomposition as the measure for the ...

In this paper, we give a characterization of strongly Jordan zero-product preserving maps on normed algebras as a generalization of  Jordan zero-product preserving maps. In this direction, we give some illustrative examples to show that the notions of strongly zero-product preserving maps and strongly Jordan zero-product preserving maps are completely different. Also, we prove that the direct p...

This paper extends the comparison results for cohomological support varieties for Chevalley groups of the form G(Fp) established by J. Carlson, Z. Lin, and D. Nakano to Chevalley groups of the form G(Fpd). Other topics considered are complexity and non-maximal support varieties for modules. Techniques developed by J. Pevtsova and the author, together with the use of Weil restriction functors, a...

This article deals with necessary and sufficient conditions for a family of elements in Euclidean Jordan algebra to have simultaneous (order) spectral decomposition. Motivated by well-known matrix theory result that any pairwise commuting complex Hermitian matrices is simultaneously (unitarily) diagonalizable, we show the setting general algebra, operator has decomposition, i.e. there exists co...

This is the rst in a series of papers dedicated to the structure of Chevalley groups over commutative rings. The goal of this series is to systematically develop methods of calculations in Chevalley groups over rings, based on the use of their minimal modules. As an application we give new direct proofs for normality of the elementary subgroup, description of normal subgroups and similar result...

We are concerned with the question when Hom-Lie structures on a Lie algebra closed respect to Jordan product. Somewhat unexpectedly, this leads us certain questions connected Yang-Baxter equation, and decomposition of into sum subalgebras given properties.