The Yang-Mills functional and Laplace's equation on quantum Heisenberg manifolds

DOI10.1016/j.jfa.2009.09.024zbMath1186.58007arXiv0904.4291OpenAlexW1964732695MaRDI QIDQ1048165

Sooran Kang

Publication date: 11 January 2010

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0904.4291

zbMATH Keywords

critical pointYang-Mills theorynoncommutative differential geometryLaplace's equationquantum Heisenberg manifold

Mathematics Subject Classification ID

Elliptic equations on manifolds, general theory (58J05) Noncommutative geometry (à la Connes) (58B34) Other ``noncommutative mathematics based on (C^*)-algebra theory (46L89) Variational problems concerning extremal problems in several variables; Yang-Mills functionals (58E15)

Related Items (7)

Subadditivity and additivity of the noncommutative Yang-Mills action functional ⋮ On the moduli space of a quantum Heisenberg manifold ⋮ Levi-Civita connections for a class of spectral triples ⋮ Yang-Mills connections on quantum Heisenberg manifolds ⋮ Yang-Mills on quantum Heisenberg manifolds ⋮ Quantum Heisenberg manifolds as twisted groupoid \(C^\ast\)-algebras ⋮ Equivalence of two approaches to Yang-Mills on noncommutative torus

Cites Work

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• Projective multi-resolution analyses for \(L^2(\mathbb R^2)\)
• Morita equivalence for crossed products by Hilbert $C^\ast $-bimodules
• "Vector bundles" over quantum Heisenberg manifolds
• Morita equivalence for quantum Heisenberg manifolds
• Introduction to M(atrix) theory and noncommutative geometry

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