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Algebraic Graph Theory
, 2011
"... Algebraic graph theory comprises both the study of algebraic objects arising in connection with graphs, for example, automorphism groups of graphs along with the use of algebraic tools to establish interesting properties of combinatorial objects. One of the oldest themes in the area is the investiga ..."
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Cited by 892 (13 self)
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Algebraic graph theory comprises both the study of algebraic objects arising in connection with graphs, for example, automorphism groups of graphs along with the use of algebraic tools to establish interesting properties of combinatorial objects. One of the oldest themes in the area
Oligomorphic permutation groups
 LONDON MATHEMATICAL SOCIETY STUDENT TEXTS
, 1999
"... A permutation group G (acting on a set Ω, usually infinite) is said to be oligomorphic if G has only finitely many orbits on Ω n (the set of ntuples of elements of Ω). Such groups have traditionally been linked with model theory and combinatorial enumeration; more recently their grouptheoretic pro ..."
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Cited by 320 (26 self)
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A permutation group G (acting on a set Ω, usually infinite) is said to be oligomorphic if G has only finitely many orbits on Ω n (the set of ntuples of elements of Ω). Such groups have traditionally been linked with model theory and combinatorial enumeration; more recently their group
Renormalization in quantum field theory and the RiemannHilbert problem. II. The βfunction, diffeomorphisms and the renormalization group
 Comm. Math. Phys
"... We show that renormalization in quantum field theory is a special instance of a general mathematical procedure of multiplicative extraction of finite values based on the Riemann–Hilbert problem. Given a loop γ(z), z  = 1 of elements of a complex Lie group G the general procedure is given by evalu ..."
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Cited by 332 (39 self)
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We show that renormalization in quantum field theory is a special instance of a general mathematical procedure of multiplicative extraction of finite values based on the Riemann–Hilbert problem. Given a loop γ(z), z  = 1 of elements of a complex Lie group G the general procedure is given
Symplectic reflection algebras, CalogeroMoser space, and deformed HarishChandra homomorphism
 Invent. Math
"... To any finite group Γ ⊂ Sp(V) of automorphisms of a symplectic vector space V we associate a new multiparameter deformation, Hκ, of the algebra C[V]#Γ, smash product of Γ with the polynomial algebra on V. The parameter κ runs over points of CP r, where r = number of conjugacy classes of symplectic ..."
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Cited by 280 (39 self)
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To any finite group Γ ⊂ Sp(V) of automorphisms of a symplectic vector space V we associate a new multiparameter deformation, Hκ, of the algebra C[V]#Γ, smash product of Γ with the polynomial algebra on V. The parameter κ runs over points of CP r, where r = number of conjugacy classes of symplectic
AUTOMORPHISMS OF FINITE ABELIAN GROUPS
"... In introductory abstract algebra classes, one typically encounters the classification of finite Abelian groups [2]: Theorem 1.1. Let G be a finite Abelian group. Then G is isomorphic to a product of groups of the form ..."
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Cited by 35 (0 self)
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In introductory abstract algebra classes, one typically encounters the classification of finite Abelian groups [2]: Theorem 1.1. Let G be a finite Abelian group. Then G is isomorphic to a product of groups of the form
FINITELY PRESENTED MVALGEBRAS WITH FINITE AUTOMORPHISM GROUP
"... Please see [1] for background on MValgebras. We address the question, which MValgebras have finite automorphism group. The automorphism group of the free MValgebra on 1 generator is just the group of order 2 (folklore). In contrast, it is known that the automorphism group of the free MValgebra o ..."
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Please see [1] for background on MValgebras. We address the question, which MValgebras have finite automorphism group. The automorphism group of the free MValgebra on 1 generator is just the group of order 2 (folklore). In contrast, it is known that the automorphism group of the free MValgebra
Automorphisms and ideals of the Weyl algebra
 Math. Ann
"... Abstract. Let A1 be the (first) Weyl algebra, and let G be its automorphism group. We study the natural action of G on the space of isomorphism classes of right ideals of A1 (equivalently, of finitely generated rank 1 torsionfree right A1modules). We show that this space breaks up into a countable ..."
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Cited by 42 (5 self)
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Abstract. Let A1 be the (first) Weyl algebra, and let G be its automorphism group. We study the natural action of G on the space of isomorphism classes of right ideals of A1 (equivalently, of finitely generated rank 1 torsionfree right A1modules). We show that this space breaks up into a
Automorphism groups of finite dimensional simple algebras
, 2002
"... We show that if a field k contains sufficiently many elements (for instance, if k is infinite), and K is an algebraically closed field containing k, then every linear algebraic kgroup over K is kisomorphic to Aut(A ⊗k K), where A is a finite dimensional simple algebra over k. ..."
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Cited by 6 (0 self)
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We show that if a field k contains sufficiently many elements (for instance, if k is infinite), and K is an algebraically closed field containing k, then every linear algebraic kgroup over K is kisomorphic to Aut(A ⊗k K), where A is a finite dimensional simple algebra over k.
Complex reflection groups, Braid groups, Hecke algebras
, 1997
"... Presentations "a la Coxeter" are given for all (irreducible) finite complex reflection groups. They provide presentations for the corresponding generalized braid groups (for all but six cases), which allow us to generalize some of the known properties of finite Coxeter groups and their a ..."
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Cited by 174 (9 self)
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and their associated braid groups, such as the computation of the center of the braid group and the construction of deformations of the finite group algebra (Hecke algebras). We introduce monodromy representations of the braid groups which factorize through the Hecke algebras, extending results of Cherednik, Opdam
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