--- title: "Beyond the 10-fold way: 13 associative Z2× Z2-graded superdivision algebras • CBPF Index" description: "CBPF INDEX es el sistema de seguimiento de la producción científica y tecnológica del CBPF. En él se puede obtener la lista de publicaciones de artículos, libros, informes técnicos, etc. de toda la comunidad del CBPF." canonical_url: "https://index.cbpf.br/es/publicacoes/6ad2a767639f62b11adbd55c" locale: es meta: "og:description": "CBPF INDEX es el sistema de seguimiento de la producción científica y tecnológica del CBPF. En él se puede obtener la lista de publicaciones de artículos, libros, informes técnicos, etc. de toda la comunidad del CBPF." "og:image": "https://index.cbpf.br/_og/d/c_Item%2Ctitulo_~QmV5b25kIHRoZSAxMC1mb2xkIHdheTogMTMgYXNzb2NpYXRpdmUgWjLDlyBaMi1ncmFkZWQgc3VwZXJkaXZpc2lvbiBhbGdlYnJhcw%2Ctipo_~Tm90YSBkZSBGw61zaWNh%2Ccor_~I2E4MmMwMA%2Cautores_~Wi4gS3V6bmV0c292YTsgRi4gVG9wcGFu%2Cdetalhe_~MDgvMTIvMjAyMQ%2Csecao_Publicaciones%2Cp_Ii9lcy9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmQ1NWMi%2Cs_Jq34Z_4tYHym1DDI.png" "og:image:height": "600" "og:image:type": image/png "og:image:width": "1200" "og:title": "Beyond the 10-fold way: 13 associative Z2× Z2-graded superdivision algebras • CBPF Index" "twitter:image": "https://index.cbpf.br/_og/d/c_Item%2Ctitulo_~QmV5b25kIHRoZSAxMC1mb2xkIHdheTogMTMgYXNzb2NpYXRpdmUgWjLDlyBaMi1ncmFkZWQgc3VwZXJkaXZpc2lvbiBhbGdlYnJhcw%2Ctipo_~Tm90YSBkZSBGw61zaWNh%2Ccor_~I2E4MmMwMA%2Cautores_~Wi4gS3V6bmV0c292YTsgRi4gVG9wcGFu%2Cdetalhe_~MDgvMTIvMjAyMQ%2Csecao_Publicaciones%2Cp_Ii9lcy9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmQ1NWMi%2Cs_Jq34Z_4tYHym1DDI.png" --- > Index of every page on this site: [llms.txt](https://index.cbpf.br/llms.txt) **Nota de Física****Publicado** # **Beyond the **101010**-fold way: **131313** associative **Z2×Z2{\\mathbb Z}\_2\\times{\\mathbb Z}\_2Z2​×Z2​**-graded superdivision algebras** **Z. Kuznetsova; F. Toppan** 08/12/2021 [**Descargar PDF **1,4 MB](https://index.cbpf.br/files/publicacao/6ad2a767639f62b11adbd55c/pdf) [**Contactar al responsable**](mailto:apub@cbpf.br?subject=Beyond%20the%2010-fold%20way%3A%2013%20associative%20Z2%C3%97%20Z2-graded%20superdivision%20algebras) ## **Datos de la publicación**
Autores
Z. Kuznetsova; F. Toppan
Tipo
Nota de Física
Estado
Publicado
Fecha de publicación
08/12/2021
Descripción
The ``$10$-fold way" refers to the combined classification of the $3$ associative division algebras (of real, complex and quaternionic numbers) and of the $7$, ${\mathbb Z}_2$-graded, superdivision algebras (in a superdivision algebra each homogeneous element is invertible). \\ The connection of the $10$-fold way with the periodic table of topological insulators and superconductors is well known. Motivated by the recent interest in ${\mathbb Z}_2\times{\mathbb Z}_2$-graded physics (classical and quantum invariant models, parastatistics) we classify the associative ${\mathbb Z}_2\times {\mathbb Z}_2$-graded superdivision algebras and show that $13$ inequivalent cases have to be added to the $10$-fold way. Our scheme is based on the ``alphabetic presentation of Clifford algebras", here extended to graded superdivision algebras. The generators are expressed as equal-length words in a $4$-letter alphabet (the letters encode a basis of invertible $2\times 2$ real matrices and in each word the symbol of tensor product is skipped). The $13$ inequivalent \zzg superdivision algebras are split into real series ($4$ subcases with $4$ generators each), complex series ($5$ subcases with $8$ generators) and quaternionic series ($4$ subcases with $16$ generators).
Año
2021
Número
CBPF-NF-004/21
Vínculo con tesis
No
Vínculo con beca
No
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