16G
Algebraic geometry
18F
03C
81R
Quantum theory (mathematics)
Mathematical logic and foundations
en
Zariski structures in noncommutative algebraic geometry and representation theory
2012-10-04T13:05:02.704Z
2011
Solanki, Vinesh
Zilber, Boris
A suitable subcategory of aﬃne Azumaya algebras is deﬁned and a functor from this category to the category of Zariski structures is constructed. The rudiments of a theory
of presheaves of topological structures is developed and applied to construct examples of structures at a generic parameter. The category of equivariant algebras is deﬁned
and a ﬁrst-order theory is associated to each object. For those theories satisfying a certain technical condition, uncountable categoricity and quantiﬁer elimination results
are established. Models are shown to be Zariski structures and a functor from the category of equivariant algebras to Zariski structures is constructed. The two functors
obtained in the thesis are shown to agree on a nontrivial class of algebras.
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born digital
2014-02-04T22:52:04.306Z
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ora:6492
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thesis