Non-commutative linear algebra and plurisubharmonic functions of quaternionic variables
نویسنده
چکیده
We remind known and establish new properties of the Dieudonné and Moore determinants of quaternionic matrices. Using these linear algebraic results we develop a basic theory of plurisubharmonic functions of quaternionic variables.
منابع مشابه
Valuations, non-commutative determinants, and quaternionic pluripotential theory.
We present a new construction of translation invariant continuous valuations on convex compact subsets of a quaternionic space H n ≃ R4n. This construction is based on the theory of plurisubharmonic functions of quaternionic variables started by the author in [4] and [5] which is based in turn on the notion of non-commutative determinants. In this paper we also establish some new properties of ...
متن کاملQuaternionic linear algebra and plurisubharmonic functions of quaternionic variables
Quaternionic linear algebra and plurisubharmonic functions of quaternionic variables. Abstract We remind known and establish new properties of the Dieudonné and Moore determinants of quaternionic matrices. Using these linear algebraic results we develop a basic theory of plurisubharmonic functions of quaternionic variables. The main point of this paper is that in quaternionic algebra and analys...
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A new method of constructing translation invariant continuous valuations on convex subsets of the quaternionic space Hn 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 developed by the author in two previous papers [5] and [6].
متن کاملA ug 2 00 4 Valuations on convex sets , non - commutative determinants , and pluripotential theory
A new method of constructing translation invariant continuous valuations on convex subsets of the quaternionic space Hn 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 developed by the author in two previous papers [5] and [6].
متن کامل1 Se p 20 06 Quaternionic plurisubharmonic functions and their applications to convexity
The goal of this article is to present a survey of the recent theory of plurisubharmonic functions of quaternionic variables, and its applications to theory of valuations on convex sets and HKT-geometry (HyperKähler with Torsion). The exposition follows the articles [4], [5], [7] by the author and [8] by M. Verbitsky and the author.
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تاریخ انتشار 2002