Toric chiral algebras
<p>In this thesis, we investigate lattice chiral algebras as defined by Beilinson and Drinfeld. Given a factorisation monoid satisfying specific conditions and a super extension of this, Beilinson and Drinfeld show that one can push forward this line bundle (super extension) to give a facto...
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| Format: | Thesis |
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2017
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| _version_ | 1826301189176688640 |
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| author | French, J |
| author2 | Kremnitzer, K |
| author_facet | Kremnitzer, K French, J |
| author_sort | French, J |
| collection | OXFORD |
| description | <p>In this thesis, we investigate lattice chiral algebras as defined by Beilinson and Drinfeld. Given a factorisation monoid satisfying specific conditions and a super extension of this, Beilinson and Drinfeld show that one can push forward this line bundle (super extension) to give a factorisation algebra. Specifically, they describe this in the case of the factorisation monoid formed by taking &Gcy;-valued divisors set-theoretically supported over each divisor, for &Gcy; a lattice, as a method of constructing these lattice chiral algebras. In this work, we show that their definitions of such divisors, and of line bundles with factorisation on these, generalise to a wider class of objects given by taking coefficients in any cone, <em>C</em>, in a lattice. We show that, in this more general case, the functors of <em>C</em>-valued divisors with settheoretic pullback contained in <em>S</em> are ind-schemes, and, from this, that they form a factorisation monoid. Further, we show that super line bundles with factorisation exist on this factorisation monoid, and that if we have a super line bundle with factorisation on the factorisation monoid of <em>C</em>-valued divisors, we can push forward such a line bundle to get a chiral (factorisation) algebra as for lattices. Hence, we obtain a new class of chiral algebras via this procedure, which we call <em>toric chiral algebras</em>.</p> |
| first_indexed | 2024-03-07T05:28:37Z |
| format | Thesis |
| id | oxford-uuid:e16ac71b-7634-48e4-971e-cda490c95f07 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T05:28:37Z |
| publishDate | 2017 |
| record_format | dspace |
| spelling | oxford-uuid:e16ac71b-7634-48e4-971e-cda490c95f072022-03-27T09:54:20ZToric chiral algebrasThesishttp://purl.org/coar/resource_type/c_db06uuid:e16ac71b-7634-48e4-971e-cda490c95f07ORA Deposit2017French, JKremnitzer, K<p>In this thesis, we investigate lattice chiral algebras as defined by Beilinson and Drinfeld. Given a factorisation monoid satisfying specific conditions and a super extension of this, Beilinson and Drinfeld show that one can push forward this line bundle (super extension) to give a factorisation algebra. Specifically, they describe this in the case of the factorisation monoid formed by taking &Gcy;-valued divisors set-theoretically supported over each divisor, for &Gcy; a lattice, as a method of constructing these lattice chiral algebras. In this work, we show that their definitions of such divisors, and of line bundles with factorisation on these, generalise to a wider class of objects given by taking coefficients in any cone, <em>C</em>, in a lattice. We show that, in this more general case, the functors of <em>C</em>-valued divisors with settheoretic pullback contained in <em>S</em> are ind-schemes, and, from this, that they form a factorisation monoid. Further, we show that super line bundles with factorisation exist on this factorisation monoid, and that if we have a super line bundle with factorisation on the factorisation monoid of <em>C</em>-valued divisors, we can push forward such a line bundle to get a chiral (factorisation) algebra as for lattices. Hence, we obtain a new class of chiral algebras via this procedure, which we call <em>toric chiral algebras</em>.</p> |
| spellingShingle | French, J Toric chiral algebras |
| title | Toric chiral algebras |
| title_full | Toric chiral algebras |
| title_fullStr | Toric chiral algebras |
| title_full_unstemmed | Toric chiral algebras |
| title_short | Toric chiral algebras |
| title_sort | toric chiral algebras |
| work_keys_str_mv | AT frenchj toricchiralalgebras |