Semantic Scholar Open Access 2011 146 sitasi

On the structure of the Witt group of braided fusion categories

A. Davydov D. Nikshych V. Ostrik

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Abstrak

We analyze the structure of the Witt group $${\mathcal{W}}$$ of braided fusion categories introduced in Davydov et al. (Journal für die reine und angewandte Mathematik (Crelle’s Journal), eprint arXiv: 1009.2117 [math.QA], 2010). We define a “super” version of the categorical Witt group, namely, the group $${s\mathcal{W}}$$ of slightly degenerate braided fusion categories. We prove that $${s\mathcal{W}}$$ is a direct sum of the classical part, an elementary Abelian 2-group, and a free Abelian group. Furthermore, we show that the kernel of the canonical homomorphism $${S : \mathcal{W} \to s\mathcal{W}}$$ is generated by Ising categories and is isomorphic to $${{\mathbb{Z}}/16\mathbb{Z}}$$ . Finally, we give a complete description of étale algebras in tensor products of braided fusion categories.

Topik & Kata Kunci

Mathematics

Penulis (3)

A. Davydov

D. Nikshych

V. Ostrik

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APA MLA BibTeX

Davydov, A., Nikshych, D., Ostrik, V. (2011). On the structure of the Witt group of braided fusion categories. https://doi.org/10.1007/S00029-012-0093-3

Akses Cepat

Lihat di Sumber doi.org/10.1007/S00029-012-0093-3

Informasi Jurnal

Tahun Terbit: 2011
Bahasa: en
Total Sitasi: 146×
Sumber Database: Semantic Scholar
DOI: 10.1007/S00029-012-0093-3
Akses: Open Access ✓