Asymptotic Behaviour of Colength of Varieties of Lie Algebras

This project was partially supported by RFBR, grants 99-01-00233, 98-01-01020 and 00-15-96128.

A Characterization of Varieties of Associative Algebras of Exponent two

∗The first author was partially supported by MURST of Italy; the second author was par- tially supported by RFFI grant 99-01-00233.

The Variety of Leibniz Algebras Defined by the Identity x(y(zt)) ≡ 0

2000 Mathematics Subject Classification: Primary: 17A32; Secondary: 16R10, 16P99, 17B01, 17B30, 20C30

Normal and Normally Outer Automorphisms of Free Metabelian Nilpotent Lie Algebras

2000 Mathematics Subject Classification: 17B01, 17B30, 17B40.

Outer endomorphisms of free metabelian Lie algebras

2000 Mathematics Subject Classification: 17B01, 17B30, 17B40.

Growth of some varieties of Leibniz-Poisson algebras

2010 Mathematics Subject Classification: 17A32, 17B63.

A Computer Algebra Application to Determination of Lie Symmetries of Partial Differential Equations

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006

M-Solid Subvarieties of some Varieties of Commutative Semigroups

∗ The research of the author was supported by the Alexander v. Humboldt-Stiftung.

Factorizations of some Groups of Lie Type of Lie Rank 4

Еленка Генчева, Цанко Генчев В настоящата работа се разглеждат крайни прости групи G , които могат да се представят като произведение на две свои собствени неабелеви прости подгрупи A и B. Всяко такова представяне G = AB е прието да се нарича факторизация на G, а тъй като множителите A и B са избрани да бъдат прости подгрупи на G, то разглежданите факторизации са известни още като прости факторизации на G. Тук се предполага, че G е проста група от лиев тип и лиев ранг 4 над крайно поле GF (q). Ключови думи: крайни прости групи, групи от лиев тип, факторизации на групи.

Canonical Objects in Classes of (n, V)-Groupoids

AMS Subj. Classification: 03C05, 08B20

Lie Groups as Four-Dimensional Special Complex Manifolds with Norden Metric

Марта Теофилова - Конструиран е пример на четиримерно специално комплексно многообразие с норденова метрика и постоянна холоморфна секционна кривина чрез двупара-метрично семейство от разрешими алгебри на Ли. Изследвани са кривинните свойства на полученото многообразие. Дадени са необходими и достатъчни усло-вия за разглежданото многообразие да бъде изотропно келерово.

q-Leibniz Algebras

2000 Mathematics Subject Classification: Primary 17A32, Secondary 17D25.

Investigating the Relations of Attacks, Methods and Objects in Regard to Information Security in Network TCP/IP Environment

Possibilities for investigations of 43 varieties of file formats (objects), joined in 10 groups; 89 information attacks, joined in 33 groups and 73 methods of compression, joined in 10 groups are described in the paper. Experimental, expert, possible and real relations between attacks’ groups, method’ groups and objects’ groups are determined by means of matrix transformations and the respective maximum and potential sets are defined. At the end assessments and conclusions for future investigation are proposed.

Exponents of Subvarieties of Upper Triangular Matrices over Arbitrary Fields are Integral

Partially supported by grant RFFI 98-01-01020.

Examples Illustrating some Aspects of the Weak Deligne-Simpson Problem

Research partially supported by INTAS grant 97-1644