Structure of free semigroupoid algebras
نویسندگان
چکیده
منابع مشابه
Free Semigroupoid Algebras
Every countable directed graph generates a Fock space Hilbert space and a family of partial isometries. These operators also arise from the left regular representations of free semigroupoids derived from directed graphs. We develop a structure theory for the weak operator topology closed algebras generated by these representations, which we call free semigroupoid algebras. We characterize semis...
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A free semigroupoid algebra is the weak operator topology closed algebra generated by the left regular representation of a directed graph. We establish lattice isomorphisms between ideals and invariant subspaces, and this leads to a complete description of the wot-closed ideal structure for these algebras. We prove a distance formula to ideals, and this gives an appropriate version of the Carat...
متن کاملSemigroupoid C*-algebras
A semigroupoid is a set equipped with a partially defined associative operation. Given a semigroupoid Λ we construct a C*-algebra O(Λ) from it. We then present two main examples of semigroupoids, namely the Markov semigroupoid associated to an infinite 0–1 matrix, and the semigroupoid associated to a higher-rank graph. In both cases the semigroupoid C*-algebra is shown to be isomorphic to the a...
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نشان می دهیم که هر اشتقاق لی روی یک c^*-جبر به شکل استاندارد است، یعنی می تواند به طور یکتا به مجموع یک اشتقاق لی و یک اثر مرکز مقدار تجزیه شود. کلمات کلیدی: اشتقاق، اشتقاق لی، c^*-جبر.
15 صفحه اولThe structure of free algebras
This article is a survey of selected results on the structure of free algebraic systems obtained during the past 50 years. The focus is on ways free algebras can be decomposed into simpler components and how the number of components and the way the components interact with each other can be readily determined. A common thread running through the exposition is a concrete method of representing a...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2019
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2019.06.002