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DTSTART:20170326T010000
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DTSTART;TZID=Europe/Paris:20170922T150000
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SUMMARY:Cayley groups
DESCRIPTION:I will start the talk with the classical Cayley transform for the special orthogonal group SO(n) defined by Arthur Cayley in 1846. A connected linear algebraic group G over a field K is called a Cayley group if it admits a Cayley map\, that is\, a G-equivariant birational isomorphism between the group variety G and its Lie algebra Lie(G). For example\, SO(n) is a Cayley group. A linear algebraic group G is called stably Cayley if G x (K*)^r is Cayley for some natural number r. I will consider semisimple algebraic groups\, in particular\, simple algebraic groups. I will describe classification of Cayley simple groups and of stably Cayley semisimple groups over an algebraically closed field of characteristic 0 (Based on joint works with Boris Kunyavskii and others).
URL:https://www.math.ens.psl.eu/evenement/cayley-groups/
LOCATION:ENS Salle W
CATEGORIES:Variétés rationnelles
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DTSTART;TZID=Europe/Paris:20170922T163000
DTEND;TZID=Europe/Paris:20170922T173000
DTSTAMP:20260408T034725
CREATED:20170922T143000Z
LAST-MODIFIED:20211104T104728Z
UID:8402-1506097800-1506101400@www.math.ens.psl.eu
SUMMARY:Algebraic structures and descent by symmetric monoidal categories and Deligne's Theory
DESCRIPTION:Let W be a finite dimensional algebraic structure over a field K of characteristic zero (for example an algebra or a graded algebra). In this talk I will explain how to construct a symmetric monoidal category CW which is (up to some categorical data) a complete invariant of W. This category will be a form of RepK-G\, where G is the algebraic group of automorphisms of W\, over some subfield K0 of K. The field K0 can be thought of as the field of invariants of W\, in a way which I will make precise.By using the theory of Deligne on symmetric monoidal categories I will show how one can use this category to construct a generic form of W\, and to study scalar invariants of W. Moreover\, I will show that forms of the structure W are in one to one correspondence with fiber functors from this category.I will give some examples of this category when W is a central simple algebra or a module over a given central simple algebra. I will also explain how one can use this category to study embeddings of projective varieties in projective spaces and study questions about field of definition.
URL:https://www.math.ens.psl.eu/evenement/algebraic-structures-and-descent-by-symmetric-monoidal-categories-and-delignes-theory/
LOCATION:ENS Salle W
CATEGORIES:Variétés rationnelles
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