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Lie Groups Quantum Mathematics Seminar

Zero-mode derivations and the completely reducibility of generalized modules for a grading-restricted vertex algebra

Yi-Zhi Huang, Rutgers University

Location:  Hill 705
Date & time: Friday, 21 September 2018 at 12:00PM - 1:00PM

  • Abstract :  I will report on the recent progress jointly wirh Qi on the cohomological criterion for the complete reducibility of generalized modules of finite length for a grading-restricted vertex algebra.
  • We found that the first cohomology of a grading-restricted vertex algebra generated by its weight-one subspace with the algebra itself as coefficients is isomorphic to its weight-one subspace. We proved that if the first cohomology of a grading-restricted vertex algebra with an arbitrary lower bounded generalized bimodule as coefficients is isomorphic to the space of what we call zero-mode derivations, then grading-restricted generalized modules satisfying the composability condition are completely reducible.

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