Abstract
In 80s physicists searched for proper superextensions of the celebrated Virasoro algebra. The resulting structures became known as superconformal algebras and attracted a lot of attention. We will discuss representations, cohomologies and further generalisations of superconformal algebras.
Talk
We will talk about Lie superalgebra (extensions of Lie-Algebra?). It was originally created as an extension of the Virasoro algebra. Taking a Grassmann-Algebra and doing an extension, we get something reminiscent of super-polynomials. Probably analogous to the Lie bracket we introduce the Poisson bracket and the Contact bracket. The bracket displays properties similar to the derivative product rule.
The talk presents a conjecture relating to superconformal algebras. Reasons to believe this conjecture are
- Fattori-Kac 2001
- Kac-Martinez-Zelmanov 2001
We define object named Cuspidal module.
According to some results we have objects which are somehow superconformal. Zelmanov presents the centralizers in his talk.
Then he presents a classification of cuspidal modules over some space. A theorem gives us such a classification.
We present some objects and give condition when the objects are cuspidal. This depends on the sum of two eigenvalues.
The mentioned earliear has been generalized by Martinez-Zelmanov 1998 to where is an associative commutative superalgebra and an even derivation.
Zelmanov presents how the product of two superalgebras induces a new contact bracket on the bracket.
We define a perfekt Lie (super)algebra if .
It would really help if I were to understand modules, fields and so on as well as I understand groups.
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