4,237 research outputs found
Abstract State Machines 1988-1998: Commented ASM Bibliography
An annotated bibliography of papers which deal with or use Abstract State
Machines (ASMs), as of January 1998.Comment: Also maintained as a BibTeX file at http://www.eecs.umich.edu/gasm
Topological Invariants For Lens Spaces And Exceptional Quantum Groups
The Reshetikhin - Turaev invariants arising from the quantum groups
associated with the exceptional Lie algebras , and at odd
roots of unity are constructed and explicitly computed for all the lens spaces.Comment: LaTeX 10 page
The N=1 triplet vertex operator superalgebras
We introduce a new family of C_2-cofinite N=1 vertex operator superalgebras
SW(m), , which are natural super analogs of the triplet vertex
algebra family W(p), , important in logarithmic conformal field
theory. We classify irreducible SW(m)-modules and discuss logarithmic modules.
We also compute bosonic and fermionic formulas of irreducible SW(m) characters.
Finally, we contemplate possible connections between the category of
SW(m)-modules and the category of modules for the quantum group
U^{small}_q(sl_2), q=e^{\frac{2 \pi i}{2m+1}}, by focusing primarily on
properties of characters and the Zhu's algebra A(SW(m)). This paper is a
continuation of arXiv:0707.1857.Comment: 53 pages; v2: references added; v3: a few changes; v4: final version,
to appear in CM
Perturbative sigma models, elliptic cohomology and the Witten genus
We provide a differential cocycle model for elliptic cohomology with complex
coefficients and use analytic methods to construct a cocycle representative for
the Witten class in this language. Our motivation stems from the conjectural
connection between 2-dimensional field theories and elliptic cohomology
originally due to G. Segal and E. Witten. The specifics of our constructions
are informed by the work of S. Stolz and P. Teichner on super Euclidean field
theories and K. Costello's construction of the Witten genus using perturbative
quantization. As a warm-up, we prove analogous results for supersymmetric
quantum mechanics and K-theory with complex coefficients.Comment: Changes made from referees suggestions: statements of main theorems
were sharpened, physical motivations were separated from the main
mathematical discussion, and the relation to Witten's original construction
was clarifie
Commutative 2-cocycles on Lie algebras
On Lie algebras, we study commutative 2-cocycles, i.e., symmetric bilinear
forms satisfying the usual cocycle equation. We note their relationship with
antiderivations and compute them for some classes of Lie algebras, including
finite-dimensional semisimple, current and Kac-Moody algebras.Comment: v7: minor changes; added ancillary file with GAP cod
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