The Algebra SeminarSpring 2011 |
The seminar meets Tuesdays in room LN 2205 at 2:50 p.m. There will be refreshments in the Anderson Reading Room at 4:00.
Organizers: Alex Feingold and Marcin Mazur
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Question. What can one say about the structure of symplectic nil-algebras, that are symplectic alternating algebras satisfying the extra law yx^n=0 for some positive integer n? In particular, does a symplectic nil-algebra have to be nilpotent?
In this talk we will try to get an answer to the question above when n=2 and n=3.
References
[1] P. Moravec and G. Traustason, Powerful 2-Engel groups, Comm. Algebra, 36 (2008), no. 11, 4096-4119.
[2] A. Tortora, M. Tota and G. Traustason, Symplectic alternating nil-algebras, submitted.
[3] G. Traustason, Powerful 2-Engel groups II, J. Algebra, 319 (2008), no. 8, 3301-3323.
[4] G. Traustason, Symplectic alternating algebras, Internat. J. Algebra Comput. 18 (2008), no. 4, 719-757.
In 1988, Frenkel, Lepowsky, and Meurman published the book called "Vertex Operator Algebras and the Monster". The goal of this book was to construct an algebraic object whose automorphism group is the Monster group. I will not be discussing the application to the Monster group in my talks, but the first seven chapters of this book provide the technical background used to construct the representations of certain affine Lie algebras.
The three goals of this talk are the following: introduce affine Lie algebras using the technique of formal variables, apply some general calculation techniques using the formal variables approach to the representation of affine Lie algebras, and construct the untwisted vertex operators to provide representations of the affine Lie algebras of types A, D, and E.
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