Filtered Lie conformal algebras whose associated graded algebras are isomorphic to that of general conformal algebra $gc_1$

Details Filtered Lie conformal algebras whose associated graded algebras are isomorphic to that of general conformal algebra $gc_1$ Filtered Lie conformal algebras whose associated graded algebras are isomorphic to that of general conformal algebra $gc_1$

2011-07-05

arxiv.org/abs/1107.0770v1

Journal of Algebra 340 (2011), 182--198

Mathematics

Quantum Algebra

Scientific paper

Let $G$ be a filtered Lie conformal algebra whose associated graded conformal algebra is isomorphic to that of general conformal algebra $gc_1$. In this paper, we prove that $G\cong gc_1$ or ${\rm gr\,}gc_1$ (the associated graded conformal algebra of $gc_1$), by making use of some results on the second cohomology groups of the conformal algebra $\fg$ with coefficients in its module $M_{b,0}$ of rank 1, where $\fg=\Vir\ltimes M_{a,0}$ is the semi-direct sum of the Virasoro conformal algebra $\Vir$ with its module $M_{a,0}$. Furthermore, we prove that ${\rm gr\,}gc_1$ does not have a nontrivial representation on a finite $\C[\partial]$-module, this provides an example of a finitely freely generated simple Lie conformal algebra of linear growth that cannot be embedded into the general conformal algebra $gc_N$ for any $N$.

Affiliated with

Also associated with

No associations

Rating

Filtered Lie conformal algebras whose associated graded algebras are isomorphic to that of general conformal algebra $gc_1$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Filtered Lie conformal algebras whose associated graded algebras are isomorphic to that of general conformal algebra $gc_1$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Filtered Lie conformal algebras whose associated graded algebras are isomorphic to that of general conformal algebra $gc_1$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-475940