197,573 research outputs found
Rings of definable scalars of Verma modules
No full textLet M be a Verma module over the Lie algebra, sl2(k), of trace zero 2×2 matrices over
the algebraically closed field k. We show that the ring, R_M, of definable scalars of M
is a von Neumann regular ring and that the canonical map from U(sl2(k)) to R_M is an
epimorphism of rings. We also describe the Ziegler closure of M. The proofs make use
of ideas from the model theory of modules
Tensor product of motives via Künneth formula
No full textFollowing Nori's original idea we here provide certain motivic categories with a canonical tensor structure. These motivic categories are associated to a cohomological functor on a suitable base category and the tensor structure is induced by the cartesian tensor structure on the base category via a cohomological Künneth formula
Model theory and modules
No full textIn recent years the interplay between model theory and other branches of mathematics has led to many deep and intriguing results. In this, the first book on the topic, the theme is the interplay between model theory and the theory of modules. The book is intended to be a self-contained introduction to the subject and introduces the requisite model theory and module theory as it is needed. Dr Prest develops the basic ideas concerning what can be said about modules using the information which may be expressed in a first-order language. Later chapters discuss stability-theoretic aspects of modul
Definable categories and T-motives
No full textMaking use of Freyd's free abelian category on a preadditive category we show that if T:D→A is a representation of a quiver D in an abelian category A then there is an abelian category A(T), a faithful exact functor FT:A(T)→A and an induced representation T~:D→A(T) such that FTT~=T universally. We then can show that T-motives as well as Nori's motives are given by a certain category of functors on definable categories
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