Semidirect products and invariant connections

DOI10.4310/PAMQ.2015.V11.N1.A1zbMATH Open1405.32024arXiv1502.05121MaRDI QIDQ315560

Indranil Biswas

Publication date: 21 September 2016

Published in: Pure and Applied Mathematics Quarterly (Search for Journal in Brave)

Abstract: Let $S$ be a complex reductive group acting holomorphically on a complex Lie group $N$ via holomorphic automorphisms. Let $K(S)subsetS$ be a maximal compact subgroup. The semidirect product $G:=NtimesK(S)$ acts on $N$ via biholomorphisms. We give an explicit description of the isomorphism classes of $G$-equivariant almost holomorphic hermitian principal bundles on $N$. Under the assumption that there is a central subgroup $Z=extU(1)$ of $K(S)$ that acts on $extLie(N)$ as multiplication through a single nontrivial character, we give an explicit description of the isomorphism classes of $G$-equivariant holomorphic hermitian principal bundles on $N$.

Full work available at URL: https://arxiv.org/abs/1502.05121

zbMATH Keywords

invariant connectionsemidirect productholomorphic Hermitian bundleparabolic subgroup

Mathematics Subject Classification ID

Local differential geometry of Hermitian and Kählerian structures (53B35) Holomorphic bundles and generalizations (32L05)

Recommendations

• Semi-direct products of Lie algebras and their invariants 👍 👎
• Connectivity of semicartesian products 👍 👎
• Semi-direct products of Lie algebras and covariants 👍 👎
• Semi-invariant product of a certain class of almost contact manifolds 👍 👎
• Title not available (Why is that?) 👍 👎
• Title not available (Why is that?) 👍 👎
• Title not available (Why is that?) 👍 👎
• Title not available (Why is that?) 👍 👎
• Title not available (Why is that?) 👍 👎
• Title not available (Why is that?) 👍 👎

This page was built for publication: Semidirect products and invariant connections

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q315560)