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Noncommutative Riemannian geometry of Kronecker algebras | | Joakim Arnlind
; | | Date: |
1 Sep 2023 | | Abstract: | 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 bimodule connections compatible with the *-structure of the
algebra. As an illustration, these concepts are applied to the noncommutative
torus where examples of torsion free and metric (Levi-Civita) connections are
given. In the main part of the paper, noncommutative geometric aspects of
(generalized) Kronecker algebras are considered. The structure of derivations
and differential calculi is explored, and torsion free bimodule connections are
studied together with their compatibility with hermitian forms, playing the
role of metrics on the module of differential forms. Moreover, for several
different choices of Lie algebras of derivations, non-trivial Levi-Civita
connections are constructed. | | Source: | arXiv, 2309.00283 | | Services: | Forum | Review | PDF | Favorites | |
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