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An introduction to noncommutative algebraic geometry
 Proceedings of the 40th Symposium on Ring Theory and Representation Theory, 53{59, Symp. Ring Theory Represent. Theory Organ. Comm
, 2008
"... Abstract. There are several research elds called noncommutative algebraic geometry. In this note, we will introduce the one founded by M. Artin. Roughly speaking, ..."
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Abstract. There are several research elds called noncommutative algebraic geometry. In this note, we will introduce the one founded by M. Artin. Roughly speaking,
Gravity and the structure of noncommutative algebras
 JHEP
"... A gravitational field can be defined in terms of a moving frame, which when made noncommutative yields a preferred basis for a differential calculus. It is conjectured that to a linear perturbation of the commutation relations which define the algebra there corresponds a linear perturbation of the g ..."
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Cited by 16 (5 self)
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A gravitational field can be defined in terms of a moving frame, which when made noncommutative yields a preferred basis for a differential calculus. It is conjectured that to a linear perturbation of the commutation relations which define the algebra there corresponds a linear perturbation
Duality in Noncommutative Algebra and Geometry
 LECTURE NOTES
, 2008
"... Duality is one of the fundamental concepts in mathematics. The most basic duality is that of linear algebra. We take a vector space V over a field K and assign to it V ∗ = HomK(V,K). If V is finite dimensional then V ∼ = V ∗∗. This can be generalized in many ways. For instance we can make V infinit ..."
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Duality is one of the fundamental concepts in mathematics. The most basic duality is that of linear algebra. We take a vector space V over a field K and assign to it V ∗ = HomK(V,K). If V is finite dimensional then V ∼ = V ∗∗. This can be generalized in many ways. For instance we can make V
Exploring noncommutative algebras
, 2005
"... In this lecture I would like to address the following question: given an associative algebra A0, what are the possible ways to deform it? Consideration of this question for concrete algebras often leads to interesting mathematical discoveries. I will discuss several approaches to this question, and ..."
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In this lecture I would like to address the following question: given an associative algebra A0, what are the possible ways to deform it? Consideration of this question for concrete algebras often leads to interesting mathematical discoveries. I will discuss several approaches to this question
Analysis and Implementation of Algorithms for Noncommutative Algebra
, 2000
"... A fundamental task of algebraists is to classify algebraic structures. For example, the classification of finite groups has been widely studied and has benefited from the use of computational tools. Advances in computer power have allowed researchers to attack problems never possible before. In thi ..."
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. In this dissertation, algorithms for noncommutative algebra, when ab is not necessarily equal to ba, are examined with practical implementations in mind. Different encodings of associative algebras and modules are also considered. To effectively analyze these algorithms and encodings, the encoding neutral analysis
Actions of Hopf algebras on noncommutative algebras ∗
"... Throughout this paper H is a finitedimensional Hopf algebra over a field k, andA is a associative kalgebra. Unless it is stated additionally, all tensor products are over k. Definition 1.1 It is said that H acts on A, if A is left Hmodule and for any h ∈ H, a, b ∈ A ..."
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Throughout this paper H is a finitedimensional Hopf algebra over a field k, andA is a associative kalgebra. Unless it is stated additionally, all tensor products are over k. Definition 1.1 It is said that H acts on A, if A is left Hmodule and for any h ∈ H, a, b ∈ A
SOME EQUIVARIANT CONSTRUCTIONS IN NONCOMMUTATIVE ALGEBRAIC GEOMETRY
, 811
"... To Mamuka Jibladze on occasion of his 50th birthday Abstract. We here present rudiments of an approach to geometric actions in noncommutative algebraic geometry, based on geometrically admissible actions of monoidal categories. This generalizes the usual (co)module algebras over Hopf algebras which ..."
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To Mamuka Jibladze on occasion of his 50th birthday Abstract. We here present rudiments of an approach to geometric actions in noncommutative algebraic geometry, based on geometrically admissible actions of monoidal categories. This generalizes the usual (co)module algebras over Hopf algebras which
Results 1  10
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37,067