The Triplet Vertex Operator Algebra $W_{(p)}$ and the Restricted Quantum Group $\bar U_{q}(sl_2)$ at $q = e ^{\pi i/p}$

Nagatomo, Kiyokazu; Tsuchiya, Akihiro

The Triplet Vertex Operator Algebra $W_{(p)}$ and the Restricted Quantum Group $\bar U_{q}(sl_2)$ at $q = e ^{\pi i/p}$

Kiyokazu Nagatomo
(
- Osaka U.
)
,
Akihiro Tsuchiya
(
- Tokyo U., IPMU
)

Feb, 2009

48 pages

e-Print:

0902.4607 [math.QA]

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Abstract: (arXiv)

We prove the abelian category of the modules over triplet VOA W(p) is category equivalent to the abelian category of the modules over quantum algebra of type sl_2 at root of unity.

References(11)

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The Triplet Vertex Operator Algebra W(p)W_{(p)}W(p)​ and the Restricted Quantum Group Uˉq(sl2)\bar U_{q}(sl_2)Uˉq​(sl2​) at q=eπi/pq = e ^{\pi i/p}q=eπi/p

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The Triplet Vertex Operator Algebra $W_{(p)}$ and the Restricted Quantum Group $\bar U_{q}(sl_2)$ at $q = e ^{\pi i/p}$