Results 21 to 30 of about 19,522 (183)
On the noncommutative geometry of square superpotential algebras
Journal of Algebra, 2012 53 pages. Final version.
Charlie Beil
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The structure of smooth algebras in Kapranov's framework for noncommutative geometry
Journal of Algebra, 2004 In Kapranov, M. {\it Noncommutative geometry based on commutator expansions,} J. reine angew. Math {\bf 505} (1998) 73-118, a theory of noncommutative algebraic varieties was proposed. Here we prove a structure theorem for the noncommutative coordinate rings of affine open subsets of such of those varieties which are smooth (Theorem 3.4).
Guillermo Cortiñas⋆
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Noncommutative Riemannian geometry of Kronecker algebras
Journal of Geometry and PhysicsWe study aspects of noncommutative Riemannian geometry of the path algebra arising from the Kronecker quiver with N arrows. To start with, the framework of derivation based differential calculi is recalled together with a discussion on metrics and bimodule connections compatible with the *-structure of the algebra.
Joakim Arnlind
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Homotopy algebras and noncommutative geometry
, 2004 We study cohomology theories of strongly homotopy algebras, namely $A_\infty, C_\infty$ and $L_\infty$-algebras and establish the Hodge decomposition of Hochschild and cyclic cohomology of $C_\infty$-algebras thus generalising previous work by Loday and Gerstenhaber-Schack. These results are then used to show that a $C_\infty$-algebra with an invariant
Alastair Hamilton, Andrey Lazarev
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Noncommutative Geometry and Gauge theories on AF algebras
, 2023 Non-commutative geometry (NCG) is a mathematical discipline developed in the 1990s by Alain Connes. It is presented as a new generalization of usual geometry, both encompassing and going beyond the Riemannian framework, within a purely algebraic formalism. Like Riemannian geometry, NCG also has links with physics.
Gaston Nieuviarts
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Noncommutative Geometry of Hensel-Steinitz Algebras
We discuss various aspects of noncommutative geometry of smooth subalgebras of Hensel-Steinitz algebras. In particular we study the structure of derivations and $K$-Theory of those smooth subalgebras.
Shelley Hebert +3 more
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Physical Review Research, 2021 With a view toward a fracton theory in condensed matter, we introduce a higher-moment polynomial degree-p global symmetry, acting on complex scalar/vector/tensor fields (e.g., ordinary or vector global symmetry for p=0 and p=1 respectively).
Juven Wang, Kai Xu, Shing-Tung Yau
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Ingeniería y Ciencia, 2020 In this paper we present a survey of some algebraic characterizations of Hilbert’s Nullstellensatz for non-commutative rings of polynomial type. Using several results established in the literature, we obtain a version of this theorem for the skew ...
Armando Reyes +1 more
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Mathematics, 2020 This paper surveys results related to well-known works of B. Plotkin and V. Remeslennikov on the edge of algebra, logic and geometry. We start from a brief review of the paper and motivations. The first sections deal with model theory.
Alexei Kanel-Belov +6 more
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Hopf Algebras, Renormalization and Noncommutative Geometry [PDF]
Communications in Mathematical Physics, 1998 We explore the relation between the Hopf algebra associated to the renormalization of QFT and the Hopf algebra associated to the NCG computations of transverse index theory for foliations.
Dirk Kreimer, Alain Connes
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