Étale groupoid algebras with coefficients in a sheaf and skew inverse semigroup rings
Keyword(s):
Abstract Given an action ${\varphi }$ of inverse semigroup S on a ring A (with domain of ${\varphi }(s)$ denoted by $D_{s^*}$ ), we show that if the ideals $D_e$ , with e an idempotent, are unital, then the skew inverse semigroup ring $A\rtimes S$ can be realized as the convolution algebra of an ample groupoid with coefficients in a sheaf of (unital) rings. Conversely, we show that the convolution algebra of an ample groupoid with coefficients in a sheaf of rings is isomorphic to a skew inverse semigroup ring of this sort. We recover known results in the literature for Steinberg algebras over a field as special cases.
1990 ◽
Vol 41
(3)
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pp. 343-346
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2000 ◽
Vol 130
(3)
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pp. 603-609
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1980 ◽
Vol 32
(6)
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pp. 1361-1371
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1988 ◽
Vol 110
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pp. 113-128
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1988 ◽
Vol 45
(3)
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pp. 372-380
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2001 ◽
Vol 64
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pp. 157-168
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