Zobrazeno 1 - 10
of 128
pro vyhledávání: '"Arnlind, Joakim"'
Autor:
Arnlind, Joakim
We 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 bi
Externí odkaz:
http://arxiv.org/abs/2309.00283
Autor:
Arnlind, Joakim, Ilwale, Kwalombota
We introduce $(\sigma,\tau)$-algebras as a framework for twisted differential calculi over noncommutative, as well as commutative, algebras with motivations from the theory of $\sigma$-derivations and quantum groups. A $(\sigma,\tau)$-algebra consist
Externí odkaz:
http://arxiv.org/abs/2207.08400
We introduce $q$-deformed connections on the quantum 2-sphere and 3-sphere, satisfying a twisted Leibniz rule in analogy with $q$-deformed derivations. We show that such connections always exist on projective modules. Furthermore, a condition for met
Externí odkaz:
http://arxiv.org/abs/2202.07331
Autor:
Arnlind, Joakim, Sykora, Andreas
We introduce shift algebras as certain crossed product algebras based on general function spaces and study properties, as well as the classification, of a particular class of modules depending on a set of matrix parameters. It turns out that the stru
Externí odkaz:
http://arxiv.org/abs/2201.04482
Autor:
Arnlind, Joakim
We study connections on hermitian modules, and show that metric connections exist on regular hermitian modules; i.e finitely generated projective modules together with a non-singular hermitian form. In addition, we develop an index calculus for such
Externí odkaz:
http://arxiv.org/abs/2102.04698
We explore the possibility of introducing q-deformed connections on the quantum 2-sphere and 3-sphere, satisfying a twisted Leibniz rule in analogy with q-deformed derivations. We show that such connections always exist on projective modules. Further
Externí odkaz:
http://arxiv.org/abs/2005.02603
Autor:
Arnlind, Joakim, Norkvist, Axel Tiger
Publikováno v:
J. Geom. Phys. 159 (2020)
In analogy with classical submanifold theory, we introduce morphisms of real metric calculi together with noncommutative embeddings. We show that basic concepts, such as the second fundamental form and the Weingarten map, translate into the noncommut
Externí odkaz:
http://arxiv.org/abs/1906.03885
We discuss quantum analogues of minimal surfaces in Euclidean spaces and tori.
Externí odkaz:
http://arxiv.org/abs/1903.10792
Autor:
Arnlind, Joakim, Landi, Giovanni
Publikováno v:
Adv. Theor. Math. Phys. 24 (2020) 527--562
We initiate a study of projections and modules over a noncommutative cylinder, a simple example of a noncompact noncommutative manifold. Since its algebraic structure turns out to have many similarities with the noncommutative torus, one can develop
Externí odkaz:
http://arxiv.org/abs/1901.07276