Spring, 2005

• Speaker L. Guo, Rutgers University at Newark
  • Title Birkhoff decomposition in QFT and CBH formula
  • Time/place Friday, 2/25/2005 3:00 pm in Hill 705
  • Abstract We discuss the Hopf algebra approach of Connes and Kreimer to renormalization in pQFT, with emphasis on the role played by the Campbell-Baker-Hausdorff formula and Rota-Baxter operator in the Birkhoff decomposition of regularized characters. We also relate this decomposition to the factorization of formal exponetials by Barron-Huang-Lepowsky and the plus-minus decomposition for combinatiral Hopf algebras by Aguiar-Sottile.

• Speaker Bin Shu, University of Virginia and East Normal University of China
  • Title Representations and Forms of Classical Lie algebras over finite fields
  • Time/place Friday, 4/8/2005 1:00 pm in Hill 525
  • Abstract By introducing Frobenius-Lie morphism, a connection between finite-dimensional representations of finite Lie algebras over finite fields and their algebraic closures is established, which enables us to understand irreducible representations of classical Lie algebras over a finite field $F_q$ through the ones of its extension over $\bar F_q$. Moreover, Frobenius-Lie morphisms provide us an approach to the determination of the number of forms of classical Lie algebras, which is different from the method used in "Modular Lie Algebras,. by G.B. Seligman. This work is done jointly with Jie Du.

• Speaker Kurusch Ebrahimi-Fard, Universitaet Bonn
  • Title Infinitesimal bialgebras and associative classical Yang-Baxter equations
  • Time/place Friday, 4/15/2005 3:00 pm in Hill 705
  • Abstract Infinitesimal bialgebras are generalized bialgebras with a comultiplication that is not an algebra homomorphism, but a derivation. They were introduced by Joni and Rota (Stud. Appl. Math. 61 (1979), no. 2, 93-139). M. Aguiar developed a theory for these objects analogous that of ordinary Hopf algebras, showed their intimate link to Rota-Baxter algebras, Loday's dendriform algebras, and introduced the associative classical Yang-Baxter equation. In this talk we will briefly review and generalize the above setting. Also, we will explore the factorization theorems related to Rota-Baxter algebras and the BCH-formula in this context.

• Speaker Kate Hurley, Pennsylvania State University
  • Title Some modular forms associated to the moonshine module
  • Time/place Friday, 4/22/2005 3:00 pm in Hill 705
  • Abstract This talk presents a brief introduction to vertex operator algebras and the moonshine module. Vertex operator algebras are modules for the Virasoro Lie algebra with Virasoro highest-weight vectors. This talk describes a family of such highest-weight vectors and finds their graded traces, also called one-point correlation functions, which are modular forms.

• Speaker Cristiano Husu, University of Connecticut, Stamford
  • Title Relative twisted vertex operators associated with the roots of the Lie algebras A_{1} and A_{2}
  • Time/place Friday, 4/29/2005 3:00 pm in Hill 705
  • Abstract The Jacobi identity for vertex operator algebras incorporates a family of "cross-brackets," including the Lie bracket, and expresses these brackets as the product of an "iterate" of vertex operators with a suitable form of the formal delta function. The generalization of the Jacobi identity to relative vertex operators requires the introduction of "correction factors" which preserve the vertex operator structure of the Jacobi identity. These correction factors, in turn, uncover the main features of Z-algebras (generalized commutator and anti-commutator relations) in the computation of a residue of the relative (twisted) Jacobi identity. More specifically, using k copies of the weight lattices of the Lie algebras A_{1} and A_{2} in the diagonal embedding, we construct relative twisted vertex operators equivalent to Z-algebra operators that determine the structure of standard A_{1}^{(1)} and A_{2}^{(2)}-modules. Applying the properties of the delta function, the corresponding generalized commutator and anti-commutator relations appear as residues of the Jacobi identity for relative twisted vertex operators.