Reflective centers of module categories and quantum K-matrices
Our work is motivated by obtaining solutions to the quantum reflection equation (qRE) by categorical methods. To start, given a braided monoidal category ${\mathcal {C}}$ and ${\mathcal {C}}$ -module category ${\mathcal {M}}$ , we introduce a version of the Drinfeld center ${\...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2025-01-01
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| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509425100558/type/journal_article |
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| Summary: | Our work is motivated by obtaining solutions to the quantum reflection equation (qRE) by categorical methods. To start, given a braided monoidal category
${\mathcal {C}}$
and
${\mathcal {C}}$
-module category
${\mathcal {M}}$
, we introduce a version of the Drinfeld center
${\mathcal {Z}}({\mathcal {C}})$
of
${\mathcal {C}}$
adapted for
${\mathcal {M}}$
; we refer to this category as the reflective center
${\mathcal {E}}_{\mathcal {C}}({\mathcal {M}})$
of
${\mathcal {M}}$
. Just like
${\mathcal {Z}}({\mathcal {C}})$
is a canonical braided monoidal category attached to
${\mathcal {C}}$
, we show that
${\mathcal {E}}_{\mathcal {C}}({\mathcal {M}})$
is a canonical braided module category attached to
${\mathcal {M}}$
; its properties are investigated in detail. |
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| ISSN: | 2050-5094 |