# On the K-theory of the ${C}^{*}$-algebra generated by the left regular representation of an Ore semigroup

Joachim Cuntz; Siegfried Echterhoff; Xin Li

Journal of the European Mathematical Society (2015)

- Volume: 017, Issue: 3, page 645-687
- ISSN: 1435-9855

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topCuntz, Joachim, Echterhoff, Siegfried, and Li, Xin. "On the K-theory of the $C^*$-algebra generated by the left regular representation of an Ore semigroup." Journal of the European Mathematical Society 017.3 (2015): 645-687. <http://eudml.org/doc/277507>.

@article{Cuntz2015,

abstract = {We compute the $K$-theory of $C^*$-algebras generated by the left regular representation of left Ore semigroups satisfying certain regularity conditions. Our result describes the $K$-theory of these semigroup $C^*$-algebras in terms of the $K$-theory for the reduced group $C^*$-algebras of certain groups which are typically easier to handle. Then we apply our result to specific semigroups from algebraic number theory.},

author = {Cuntz, Joachim, Echterhoff, Siegfried, Li, Xin},

journal = {Journal of the European Mathematical Society},

keywords = {$K$-theory; semigroup $C^*$-algebra; $ax + b$-semigroup; purely infinite; left Ore semigroup; -theory; reduced semigroup -algebra; left Ore semigroup},

language = {eng},

number = {3},

pages = {645-687},

publisher = {European Mathematical Society Publishing House},

title = {On the K-theory of the $C^*$-algebra generated by the left regular representation of an Ore semigroup},

url = {http://eudml.org/doc/277507},

volume = {017},

year = {2015},

}

TY - JOUR

AU - Cuntz, Joachim

AU - Echterhoff, Siegfried

AU - Li, Xin

TI - On the K-theory of the $C^*$-algebra generated by the left regular representation of an Ore semigroup

JO - Journal of the European Mathematical Society

PY - 2015

PB - European Mathematical Society Publishing House

VL - 017

IS - 3

SP - 645

EP - 687

AB - We compute the $K$-theory of $C^*$-algebras generated by the left regular representation of left Ore semigroups satisfying certain regularity conditions. Our result describes the $K$-theory of these semigroup $C^*$-algebras in terms of the $K$-theory for the reduced group $C^*$-algebras of certain groups which are typically easier to handle. Then we apply our result to specific semigroups from algebraic number theory.

LA - eng

KW - $K$-theory; semigroup $C^*$-algebra; $ax + b$-semigroup; purely infinite; left Ore semigroup; -theory; reduced semigroup -algebra; left Ore semigroup

UR - http://eudml.org/doc/277507

ER -

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