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The Local Multiplier Algebra of a C*-Algebra, II

✍ Scribed by D.W.B. Somerset

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
193 KB
Volume
171
Category
Article
ISSN
0022-1236

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✦ Synopsis

Let A be a separable C*-algebra and let M loc (A) be the local multiplier algebra of A. It is shown that every minimal closed prime ideal of M loc (A) is primitive. If Prim(A) has a dense G $ consisting of closed points (for instance, if Prim(A) is a T 1 -space) and A is unital, then M loc (A) is its own local multiplier algebra and has only inner derivations. The same is true for

) is the regular _-completion of A, which is an AW*-algebra.

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## Let be a basic representation-finite biserial finite-dimensional k-algebra. We describe a method for constructing a multiplicative basis and the bound quiver of the Ext-algebra E = mβ‰₯0 Ext m /r /r of using the Auslander-Reiten quiver of .