Valuations on convex sets, non-commutative determinants, and pluripotential theory

Semyon Alesker

Valuations on convex sets, non-commutative determinants, and pluripotential theory

Metric Geometry 2016-07-06 v5 Complex Variables

Authors: Semyon Alesker

Abstract

A new method of constructing translation invariant continuous valuations on convex subsets of the quaternionic space $\HH^n$ is presented. In particular new examples of $Sp(n)Sp(1)$ -invariant translation invariant continuous valuations are constructed. This method is based on the theory of plurisubharmonic functions of quaternionic variables.

Keywords

invariant theory

Cite

@article{arxiv.math/0401219,
  title  = {Valuations on convex sets, non-commutative determinants, and pluripotential theory},
  author = {Semyon Alesker},
  journal= {arXiv preprint arXiv:math/0401219},
  year   = {2016}
}

Comments

39 pages. The definition of the quaternionic Hessian is replaced with the transposed matrix as it should be

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