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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 geome-try. In this note, we will introduce the one founded by M. Artin. Roughly speaking, ..."
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Cited by 2 (0 self)
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Abstract. There are several research elds called noncommutative algebraic geome-try. 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
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
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
Analysis and Implementation of Algorithms for Noncommutative Algebra
, 2000
"... A fundamental task of algebraists is to classify algebraic structures. For example, the classifica-tion 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 finite-dimensional Hopf algebra over a field k, andA is a associative k-algebra. 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 H-module and for any h ∈ H, a, b ∈ A ..."
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Throughout this paper H is a finite-dimensional Hopf algebra over a field k, andA is a associative k-algebra. 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 H-module and for any h ∈ H, a, b ∈ A
SOME EQUIVARIANT CONSTRUCTIONS IN NONCOMMUTATIVE ALGEBRAIC GEOMETRY
, 2009
"... 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 provide affine examples. We introduce a compatibility of mono ..."
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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 provide affine examples. We introduce a compatibility
Differential and holomorphic differential operators on noncommutative algebras
, 2015
"... Abstract This paper deals with sheaves of differential operators on noncommutative algebras, in a manner related to the classical theory of D-modules. The sheaves are defined by quotienting the tensor algebra of vector fields (suitably deformed by a covariant derivative). As an example we can obtai ..."
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Abstract This paper deals with sheaves of differential operators on noncommutative algebras, in a manner related to the classical theory of D-modules. The sheaves are defined by quotienting the tensor algebra of vector fields (suitably deformed by a covariant derivative). As an example we can
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