Coset vertex operator algebras and W-algebras of A-type
| Autor: | Cuipo Jiang, Tomoyuki Arakawa |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
Generator (category theory) General Mathematics 010102 general mathematics 01 natural sciences Centralizer and normalizer Vertex (geometry) Operator algebra Vertex operator algebra 0103 physical sciences Lie algebra 010307 mathematical physics Nest algebra 0101 mathematics Coxeter element Mathematics |
| Zdroj: | Science China Mathematics. 61:191-206 |
| ISSN: | 1869-1862 1674-7283 |
| DOI: | 10.1007/s11425-017-9161-7 |
| Popis: | We give an explicit description for a weight three generator of the coset vertex operator algebra $C_{L_{\widehat{\sl_{n}}}(l,0)\otimes~L_{\widehat{\sl_{n}}}(1,0)}(L_{\widehat{\sl_{n}}}(l+1,0))$, for $n\geq~2$, $l\geq~1$. Furthermore, we prove that the commutant $C_{L_{\widehat{\sl_{3}}}(l,0)\otimes~L_{\widehat{\sl_{3}}}(1,0)}(L_{\widehat{\sl_{3}}}(l+1,0))$ is isomorphic to the $\W$-algebra $\W_{-3+\frac{l+3}{l+4}}(\sl_3)$, which confirms the conjecture for the $\sl_3$ casethat $C_{L_{\widehat{\frak~g}}(l,0)\otimes~L_{\widehat{\frak~g}}(1,0)}(L_{\widehat{\frak~g}}(l+1,0))$ is isomorphic to$\W_{-h+\frac{l+h}{l+h+1}}(\frak~g)$ for simply-laced Lie algebras ${\frak~g}$ with its Coxeter number $h$ for a positive integer $l$. |
| Databáze: | OpenAIRE |
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