Type: Seminar

Distribution: World

Expiry: 5 Aug 2008

Auth: anthonyh@asti.maths.usyd.edu.au

THE UNIVERSITY OF NEW SOUTH WALES DEPARTMENT OF PURE MATHEMATICS _________________DEPARTMENTAL SEMINAR__________________ Speaker: Christopher Drupieski (Virginia) Title: Cohomology of infinitesimal algebraic groups and quantized enveloping algebras Date: Tuesday, 5 August 2008 Time: 12:00 noon Venue: RC-3084, The Red Centre, UNSW Abstract: In 1984, Andersen and Jantzen computed the structure of the cohomology ring with trivial coefficients of the restricted Lie algebra corresponding to a reductive algebraic group. In 1993, Ginzburg and Kumar adapted the arguments of Andersen and Jantzen to compute the cohomology ring with trivial coefficients of the finite-dimensional quantum enveloping algebra at an ell-th root of unity defined by Lusztig. In both cases, lower bounds were assumed on the characteristic p of the ground field (respectively, the order ell of the root of unity) in order to achieve key vanishing results. Beyond some ad hoc calculations by Andersen and Jantzen, general results for small values of p and ell remained elusive. In this talk I will report on some recent results of Bendel, Nakano, Parshall and Pillen that provide a uniform method for computing the aforementioned cohomology groups, as well as some recent results and some open questions in the quantum mixed case. Related results on the coordinate rings of nilpotent varieties may also be touched upon. Some basic familiarity with group theory and Lie algebras will be assumed (e.g., root space decomposition). I will endeavor to present the remaining content on algebraic groups, Frobenius kernels, spectral sequences, and quantized enveloping algebras in a sufficiently elementary fashion that no previous mastery of these topics will be assumed. Enquiries to Jonathan Kress, 9385 7078, j.kress@unsw.edu.au