Seminario de Algebra
Sobre el Seminario
El objetivo del Seminario de Algebra del Departamento de Matemática es promover el intercambio de ideas entre matemáticos interesados en el Algebra, entendida en un sentido amplio. Los tópicos de interés de los participantes son variados e incluyen Algebra Homológica, Geometría Algebraica, Topología Algebraica, Física Teórica, Teoría de Números, etc.
Las exposiciones tratan sobre temas de investigación propios de los participantes, introducciones elementales a temas centrales o reportes sobre trabajos importantes de interés general.
Las reuniones tienen lugar generalmente en el aula de seminario del departamento, los días jueves a las 14:00hs, aproximadamente cada 15 días.
Próxima charla:
7 de diciembre, 14:00
Plamen Koshlukov (Universidad de Campinas, Brasil)
Involutions on the algebra of upper triangular matrices over an infinite field
The involutions on a central simple algebra were described by A. Albert. It is known that if R is the algebra of all n⨉n matrices over an algebraically closed field then there exist, up to isomorphism, only two involutions for R, namely the usual transpose involution, and if n is even, the usual symplectic involution. The talk will be concerned with an analogous question about the algebra of upper triangular matrices over an infinite field of characteristic different from two. The main result to be discussed is that the only involutions on this algebra are the ones induced by involutions on the corresponding full matrix algebra. In particular one has that studying polynomial identities with involution for this algebra one may work with the analogs of the transpose and the symplectic involutions only, as it is the case with the full matrix algebra.
In order to obtain the main result mentioned above one needs detailed information about the existence of certain “good” central idempotents that are fixed by the involution. Furthermore one uses ideas from structure theory of associative algebras as well as combinatorics and linear algebra.