Noncommutative differential geometry, and the matrix representations of generalised algebras [PDF]
Journal of Geometry and Physics, 1998 16 pages Latex, No figures.
Jonathan Gratus
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Geometry of differential operators, odd Laplacians, and homotopy algebras [PDF]
Journal of Nonlinear Mathematical Physics, 2004 We give a complete description of differential operators generating a given bracket. In particular we consider the case of Jacobi-type identities for odd operators and brackets. This is related with homotopy algebras using the derived bracket construction. (Based on a talk at XXII Workshop on Geometric Methods in Physics at Bialowieza)
H. M. Khudaverdian, Theodore Voronov
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Noncommutative differential geometry on crossed product algebras
Journal of Algebra, 2023 We provide a differential structure on arbitrary cleft extensions $B:=A^{\mathrm{co}H}\subseteq A$ for an $H$-comodule algebra $A$. This is achieved by constructing a covariant calculus on the corresponding crossed product algebra $B\#_σH$ from the data of a bicovariant calculus on the structure Hopf algebra $H$ and a calculus on the base algebra $B ...
Andrea Sciandra, Thomas Weber
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Nonsmooth differential geometry and algebras of generalized functions
Journal of Mathematical Analysis and Applications, 2004 17 pages, typos ...
Michael Kunzinger
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Differential Bundles in Commutative Algebra and Algebraic Geometry
, 2023 In this paper, we explain how the abstract notion of a differential bundle in a tangent category provides a new way of thinking about the category of modules over a commutative ring and its opposite category. MacAdam previously showed that differential bundles in the tangent category of smooth manifolds are precisely smooth vector bundles.
G. S. H. Cruttwell +1 more
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Jacobian problems in differential equations and algebraic geometry
Rocky Mountain Journal of Mathematics, 1982 One of these problems, described in §3, concerns polynomial transformations (i.e., transformations T where P and Q are polynomials in x and y) and, hence, is of interest to algebraic geometers, although they would prefer to consider transformations of C.
G. Meisters
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Quantum Observables Algebras and Abstract Differential Geometry: The Topos-Theoretic Dynamics of Diagrams of Commutative Algebraic Localizations [PDF]
, 2004 We construct a sheaf-theoretic representation of quantum observables algebras over a base category equipped with a Grothendieck topology, consisting of epimorphic families of commutative observables algebras, playing the role of local arithmetics in ...
Elias Zafiris
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Differential geometry of the Lie algebra of the quantum plane [PDF]
Czechoslovak Journal of Physics, 2005 11 pages, no ...
Salih Çelïk, Sultan A. Çelik
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Differential Geometry Revisited by Biquaternion Clifford Algebra [PDF]
, 2015 In the last century, differential geometry has been expressed within various calculi: vectors, tensors, spinors, exterior differential forms and recently Clifford algebras. Clifford algebras yield an excellent representation of the rotation group and of the Lorentz group which are the cornerstones of the theory of moving frames.
Patrick Girard +4 more
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Linear algebra and differential geometry on abstract Hilbert space [PDF]
International Journal of Mathematics and Mathematical Sciences, 2005 Isomorphisms of separable Hilbert spaces are analogous to isomorphisms of n‐dimensional vector spaces. However, while n‐dimensional spaces in applications are always realized as the Euclidean space Rn, Hilbert spaces admit various useful realizations as spaces of functions.
Alexey A. Kryukov
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