UTA Department of Mathematics

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Metroplex Algebraic Geometry, Algebra and Number Theory (AGANT) Seminar,
a joint venture of   UNT,   UTA   and   TCU

Date/Time/Room: Friday (10/19/2012) at 4:30 pm in 311 Pickard Hall

Speaker: Prof. Charles Conley,
Department of Mathematics, University of North Texas.

"Representations of Vector Field Lie Algebras"

Abstract:This talk will be an introduction to representations of Lie algebras of vector fields on Euclidean spaces. We will focus mainly on the simplest example, the Lie algebra Vec(R) of vector fields on the line. Although this algebra may be defined relatively simply, its representation theory is intricate and has been the topic of a considerable amount of research over the past two decades. Some of the important objects in the area are the tensor density modules, which are deformations of the natural action of Vec(R) on the space of functions and yield all of the irreducible admissible modules, and the differential operator modules, which provide examples of cohomology classes "in nature". A crucial tool in studying these representations is the projective subalgebra, which consists of the infinitesimal linear fractional transformations and is a copy of sl(2).

We will describe some of the results which have been obtained in the 1-dimensional case, and mention the status of the analogous questions in higher dimensions, where much less is known. We will try to make the talk accessible to non-specialists and graduate students: in particular, we will not assume any prior knowledge of Lie algebras or their representations.

A map of UTA may be found at http://www.uta.edu/maps/, and at http://www.uta.edu/maps/transportation. The former gives buildings and the latter gives parking lots; both are interactive.
Note that PKH is the triangular building in the 3 pm position in the former. Select Pickard Hall from the building selector. PKH is next to the ``garage'' & is on Nedderman Dr between Planatarium Place (aka College St) & West St. West St is one-way northbound between W Mitchell St and 3rd St. Parking is available in the nearby (East and SE of PKH) parking lots with a UTA permit (but many people park there late on Fridays with no permit). There are a few metered parking spots on the East side of Pickard Hall on West St. Visitor (free), & metered, parking is available by Davis Hall (marked DH in SW part of the submap). A parking garage (expensive) is nextdoor to PKH (use West St to get to it). Note that if heading south on Cooper, then no left turn is allowed to Nedderman Dr.
Note that PKH 311 is on the 3rd floor of PKH; turn LEFT out of elevator on 3rd floor to end of hall, left again towards the end of that hall, and 311 will be on your right-hand side.

Questions, etc on arrangements/directions should be sent to Dr Vancliff; if travelling from out of town, notify Dr Vancliff, as we will delay starting the talk for you if you are late.

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