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Non-commutative linear algebra and plurisubharmonic functions of quaternionic variables

Semyon Alesker
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Abstract

We recall known and establish new properties of the Dieudonn\'e and Moore determinants of quaternionic matrices.Using these linear algebraic results we develop a basic theory of plurisubharmonic functions of quaternionic variables. Then we introduce and briefly discuss quaternionic Monge-Amp\'ere equations.

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Semyon Alesker. 2001-04-23. Non-commutative linear algebra and plurisubharmonic functions of quaternionic variables. https://arxiv.org/abs/math/0104209

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