text
thesis
2012-10-04T13:05:02.704Z
ora:6492
2011
2014-02-04T22:52:04.306Z
en
fedoraAdmin
81R
Quantum theory (mathematics)
03C
Algebraic geometry
16G
18F
Mathematical logic and foundations
Zariski structures in noncommutative algebraic geometry and representation theory
Zilber, Boris
Solanki, Vinesh
born digital
urn:uuid:3fa23b75-9b85-4dc2-9ad6-bdb20d61fe45
ora:6492
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.