Punita Batra


Research Summary:

In a joint work with Prof. Stephen Berman, I tried to find the generators and relations of Intersection matrix algebras of type sl3(R[2]), where R[2] is the ${\Bbb C}$-algebra of Laurent polynomials in the 2 non-commuting variables t1,t2. This work is still going on. For a definition of Intersection matrix algebras of type sl3(R[2]), one can see the paper "Lie Algebras graded by finite root systems and the intersection matrix algebras of Slodowy" by Berman and Moody, Inventiones Mathematicae, 108, 323-347(1992).

In another project with Prof. S. Eswara Rao, I tried to prove if $\mathfrak g$ is a centerless Lie-n-tori of type Bn , then $\mathfrak g$ is isogenous to twisted multi loop Lie algebra. I am trying to prove the similar results for centerless Lie-n-tori of type F4 and G2 .

Publications:

Representations of twisted multi-loop Lie algebras, Journal of Algebra, 272(404-416), 2004.

Preprints:

  1. Integrable modules for the twisted affine Kac-moody Lie algebras, In Preparation.
  2. (With S. Eswara Rao) Realization of Lie-n-tori of type Bn ,F4 and G2 , In Preparation.

Conference/Workshops Attended:

  1. Workshop and Conference on Infinite Dimensional Lie Theory and its Applications, The Fields Institute, Toronto, July 17-25, 2003.
  2. International Colloquium on "Algebraic Groups and Homogeneous Spaces, TIFR, Bombay, January 6-14, 2004.

Visits to other Institutes:

  1. Visited University of Saskatoon, Canada from June 23 - July 13, 2003.
  2. Visited The Fields Institute, Toronto, Canada from July 14 - July 24, 2004.

Invited Lectures/Seminars:

  1. Representations of twisted multi loop Lie algebras in The Fields Institite, Toronto on July 21, 2003.
Other Activities:
  1. Gave a series of five lectures on "Bilinear Forms and Lie Algebras" at HRI in VSSP programme in May 2003. 2) Gave two lectures on "Quadratic Inequalities" in Hindi in the Rajbhasha programme organised by Dr. V. Singh in May 2003.
  2. Gave first year graduate course "Algebra" in Fall semester 2003.
  3. Coordinator JEST(Mathematics) 2004 exam, at H. R. I.


© Harish-Chandra Research Institute