Hall algebras and the Quantum Frobenius
Lusztig has constructed a Frobenius morphism for quantum groups at an $\ell$-th root of unity, which gives an integral lift of the Frobenius map on universal enveloping algebras in positive characteristic. Using the Hall algebra we give a simple construction of this map for the positive part of the...
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| Format: | Journal article |
| Language: | English |
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2006
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| _version_ | 1797079445595488256 |
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| author | McGerty, K |
| author_facet | McGerty, K |
| author_sort | McGerty, K |
| collection | OXFORD |
| description | Lusztig has constructed a Frobenius morphism for quantum groups at an $\ell$-th root of unity, which gives an integral lift of the Frobenius map on universal enveloping algebras in positive characteristic. Using the Hall algebra we give a simple construction of this map for the positive part of the quantum group attached to an arbitrary Cartan datum in the nondivisible case. |
| first_indexed | 2024-03-07T00:45:57Z |
| format | Journal article |
| id | oxford-uuid:84aaba8c-de2e-4b6b-b819-a012eee07b24 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T00:45:57Z |
| publishDate | 2006 |
| record_format | dspace |
| spelling | oxford-uuid:84aaba8c-de2e-4b6b-b819-a012eee07b242022-03-26T21:52:33ZHall algebras and the Quantum FrobeniusJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:84aaba8c-de2e-4b6b-b819-a012eee07b24EnglishSymplectic Elements at Oxford2006McGerty, KLusztig has constructed a Frobenius morphism for quantum groups at an $\ell$-th root of unity, which gives an integral lift of the Frobenius map on universal enveloping algebras in positive characteristic. Using the Hall algebra we give a simple construction of this map for the positive part of the quantum group attached to an arbitrary Cartan datum in the nondivisible case. |
| spellingShingle | McGerty, K Hall algebras and the Quantum Frobenius |
| title | Hall algebras and the Quantum Frobenius |
| title_full | Hall algebras and the Quantum Frobenius |
| title_fullStr | Hall algebras and the Quantum Frobenius |
| title_full_unstemmed | Hall algebras and the Quantum Frobenius |
| title_short | Hall algebras and the Quantum Frobenius |
| title_sort | hall algebras and the quantum frobenius |
| work_keys_str_mv | AT mcgertyk hallalgebrasandthequantumfrobenius |