Orthogonality: An antidote to Kadison's anti-lattice theorem
Anil Kumar Karn
TL;DR
This paper introduces non-commutative analogues of infimum and supremum using algebraic orthogonality to address limitations related to Kadison's anti-lattice theorem.
Contribution
It presents a novel approach to defining lattice operations in non-commutative settings through algebraic orthogonality.
Findings
New definitions of infimum and supremum in non-commutative algebra
Addresses limitations of Kadison's anti-lattice theorem
Provides a framework for non-commutative lattice theory
Abstract
In this paper, we propose non-commutative analogues of infimum and supremum with the help of algebraic orthogonality.
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Taxonomy
TopicsAdvanced Algebra and Logic · Logic, Reasoning, and Knowledge · semigroups and automata theory