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11	On the Conjugacy of Maximal Toral Subalgebras of Certain Infinite-Dimensional Lie Algebras Gontcharov, Aleksandr 10 September 2013 (has links) We will extend the conjugacy problem of maximal toral subalgebras for Lie algebras of the form $\g{g} \otimes_k R$ by considering $R=k[t,t^{-1}]$ and $R=k[t,t^{-1},(t-1)^{-1}]$, where $k$ is an algebraically closed field of characteristic zero and $\g{g}$ is a direct limit Lie algebra. In the process, we study properties of infinite matrices with entries in a B\'zout domain and we also look at how our conjugacy results extend to universal central extensions of the suitable direct limit Lie algebras. Lie algebras representation theory Bezout domains Bezout Rings central extensions conjugacy problem direct limit lie algebras maximal toral subalgebra cartan subalgebra finitely generated bezout domain
12	On the Conjugacy of Maximal Toral Subalgebras of Certain Infinite-Dimensional Lie Algebras Gontcharov, Aleksandr January 2013 (has links) We will extend the conjugacy problem of maximal toral subalgebras for Lie algebras of the form $\g{g} \otimes_k R$ by considering $R=k[t,t^{-1}]$ and $R=k[t,t^{-1},(t-1)^{-1}]$, where $k$ is an algebraically closed field of characteristic zero and $\g{g}$ is a direct limit Lie algebra. In the process, we study properties of infinite matrices with entries in a B\'zout domain and we also look at how our conjugacy results extend to universal central extensions of the suitable direct limit Lie algebras. Lie algebras representation theory Bezout domains Bezout Rings central extensions conjugacy problem direct limit lie algebras maximal toral subalgebra cartan subalgebra finitely generated bezout domain
13	Centra of Quiver Algebras Gawell, Elin January 2014 (has links) A partly (anti-)commutative quiver algebra is a quiver algebra bound by an (anti-)commutativity ideal, that is, a quadratic ideal generated by monomials and (anti-)commutativity relations. We give a combinatorial description of the ideals and the associated generator graphs, from which one can quickly determine if the ideal is admissible or not. We describe the center of a partly (anti-)commutative quiveralgebra and state necessary and sufficient conditions for the center to be finitely genteratedas a K-algebra.Examples are provided of partly (anti-)commutative quiver algebras that are Koszul algebras. Necessary and sufficient conditions for finite generation of the Hochschild cohomology ring modulo nilpotent elements for a partly (anti-)commutative Koszul quiver algebra are given. quiver algebra commutativity ideal anti-commutativity ideal non-commutative partly commutative partly anti-commutative center Koszul algebra finitely generated graded center Hochschild cohomology support variety associative algebra Mathematics Matematik
14	Unique Prime Factorization of Ideals in the Ring of Algebraic Integers of an Imaginary Quadratic Number Field Rezola, Nolberto 01 June 2015 (has links) The ring of integers is a very interesting ring, it has the amazing property that each of its elements may be expressed uniquely, up to order, as a product of prime elements. Unfortunately, not every ring possesses this property for its elements. The work of mathematicians like Kummer and Dedekind lead to the study of a special type of ring, which we now call a Dedekind domain, where even though unique prime factorization of elements may fail, the ideals of a Dedekind domain still enjoy the property of unique prime factorization into a product of prime ideals, up to order of the factors. This thesis seeks to establish the unique prime ideal factorization of ideals in a special type of Dedekind domain: the ring of algebraic integers of an imaginary quadratic number field. imaginary quadratic number field unique prime ideal factorization Dedekind domain Algebraic integers Rings Fields Ideals Integral over R-modules finitely generated set UFD PID. Algebra Number Theory Other Mathematics

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