BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Claudemir Fideles (University of Campinas\, Brazil) DTSTART:20240603T150000Z DTEND:20240603T160000Z DTSTAMP:20260423T021129Z UID:ENAAS/73 DESCRIPTION:Title: G raded identities in Lie algebras with Cartan gradings: an algorithm\nb y Claudemir Fideles (University of Campinas\, Brazil) as part of European Non-Associative Algebra Seminar\n\n\nAbstract\nThe classification of finit e-dimensional semisimple Lie algebras in characteristic 0 represents one o f the significant achievements in algebra during the first half of the 20t h century. This classification was developed by Killing and by Cartan. Acc ording to the Killing–Cartan classification\, the isomorphism classes of simple Lie algebras over an algebraically closed field of characteristic zero correspond one-to-one with irreducible root systems. In the infinite- dimensional case the situation is more complicated\, and the so-called alg ebras of Cartan type appear. It is somewhat surprising that graded identit ies for Lie algebras have been relatively few results to that extent. In t his presentation\, we will discuss some of the results obtained thus far a nd introduce an algorithm capable of generating a basis for all graded ide ntities in Lie algebras with Cartan gradings. Specifically\, over any infi nite field\, we will apply this algorithm to establish a basis for all gra ded identities of $U_1$\, the Lie algebra of derivations of the algebra of Laurent polynomials $K[t\,t^{-1}]$]\, and demonstrate that they do not a dmit any finite basis. The findings discussed in this presentation are joi nt works with P. Koshlukov (UNICAMP).\n LOCATION:https://researchseminars.org/talk/ENAAS/73/ END:VEVENT END:VCALENDAR