Derived counterparts of fusion categories of quantum groups

Juan Camilo Arias

doi:10.1016/j.jalgebra.2020.07.004

Derived counterparts of fusion categories of quantum groups

Juan Camilo Arias

Research output: Contribution to Journal › Research Article › peer-review

Abstract

In this paper, we study derived versions of the fusion category associated to Lusztig's quantum group U_q. The categories that arise in this way are not semisimple but recovers the usual fusion ring when passing to Grothendieck rings. On the derived level it turns out that it is possible to define fusion for U_q without using the notion of tilting modules. Hence, we arrive at a definition of the fusion ring that makes sense in any spherical category. We apply this new definition to the small quantum group and we relate it with some rings appearing in [22].

Original language	English (US)
Pages (from-to)	257-285
Number of pages	29
Journal	Journal of Algebra
Volume	562
DOIs	https://doi.org/10.1016/j.jalgebra.2020.07.004
State	Published - Nov 15 2020
Externally published	Yes

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 1 No Poverty

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

Access to Document

10.1016/j.jalgebra.2020.07.004

Cite this

@article{2cd4b60918af4194b2c79581837a657d,

title = "Derived counterparts of fusion categories of quantum groups",

abstract = "In this paper, we study derived versions of the fusion category associated to Lusztig's quantum group Uq. The categories that arise in this way are not semisimple but recovers the usual fusion ring when passing to Grothendieck rings. On the derived level it turns out that it is possible to define fusion for Uq without using the notion of tilting modules. Hence, we arrive at a definition of the fusion ring that makes sense in any spherical category. We apply this new definition to the small quantum group and we relate it with some rings appearing in [22].",

author = "Arias, \{Juan Camilo\}",

note = "Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",

year = "2020",

month = nov,

day = "15",

doi = "10.1016/j.jalgebra.2020.07.004",

language = "English (US)",

volume = "562",

pages = "257--285",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Derived counterparts of fusion categories of quantum groups

AU - Arias, Juan Camilo

PY - 2020/11/15

Y1 - 2020/11/15

N2 - In this paper, we study derived versions of the fusion category associated to Lusztig's quantum group Uq. The categories that arise in this way are not semisimple but recovers the usual fusion ring when passing to Grothendieck rings. On the derived level it turns out that it is possible to define fusion for Uq without using the notion of tilting modules. Hence, we arrive at a definition of the fusion ring that makes sense in any spherical category. We apply this new definition to the small quantum group and we relate it with some rings appearing in [22].

AB - In this paper, we study derived versions of the fusion category associated to Lusztig's quantum group Uq. The categories that arise in this way are not semisimple but recovers the usual fusion ring when passing to Grothendieck rings. On the derived level it turns out that it is possible to define fusion for Uq without using the notion of tilting modules. Hence, we arrive at a definition of the fusion ring that makes sense in any spherical category. We apply this new definition to the small quantum group and we relate it with some rings appearing in [22].

UR - https://www.scopus.com/pages/publications/85087938793

UR - https://www.scopus.com/pages/publications/85087938793#tab=citedBy

U2 - 10.1016/j.jalgebra.2020.07.004

DO - 10.1016/j.jalgebra.2020.07.004

M3 - Research Article

AN - SCOPUS:85087938793

SN - 0021-8693

VL - 562

SP - 257

EP - 285

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Derived counterparts of fusion categories of quantum groups

Abstract

UN SDGs

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this