Zobrazeno 1 - 10
of 42
pro vyhledávání: '"Sørensen, Adam P. W."'
We investigate polynomial endomorphisms of graph $C^*$-algebras and Leavitt path algebras. To this end, we define and analyze the coding graph corresponding to each such an endomorphism. We find an if and only if condition for the endomorphism to res
Externí odkaz:
http://arxiv.org/abs/1810.05230
Publikováno v:
Advances in Mathematics, Vol. 373, 2020
A group may be considered $C^*$-stable if almost representations of the group in a $C^*$-algebra are always close to actual representations. We initiate a systematic study of which discrete groups are $C^*$-stable or only stable with respect to some
Externí odkaz:
http://arxiv.org/abs/1808.06793
Publikováno v:
Duke Math. J. Vol. 170 (2021), no. 11, pp. 2421-2517
We provide a complete classification of the class of unital graph $C^*$-algebras - prominently containing the full family of Cuntz-Krieger algebras - showing that Morita equivalence in this case is determined by ordered, filtered $K$-theory. The clas
Externí odkaz:
http://arxiv.org/abs/1611.07120
Publikováno v:
2016 MATRIX annals, pp. 229-249, MATRIX Book Ser., 1, Springer, Cham, 2018
We introduce filtered algebraic $K$-theory of a ring $R$ relative to a sublattice of ideals. This is done in such a way that filtered algebraic $K$-theory of a Leavitt path algebra relative to the graded ideals is parallel to the gauge invariant filt
Externí odkaz:
http://arxiv.org/abs/1610.02232
Publikováno v:
Canad. J. Math. 70 (2018), no. 2, 294-353
We address the classification problem for graph $C^*$-algebras of finite graphs (finitely many edges and vertices), containing the class of Cuntz-Krieger algebras as a prominent special case. Contrasting earlier work, we do not assume that the graphs
Externí odkaz:
http://arxiv.org/abs/1604.05439
Autor:
Brownlowe, Nathan, Sørensen, Adam P W
Publikováno v:
Journal of Algebra, Volume 456, 15 June 2016, Pages 1-22
For a commutative ring $R$ with unit we investigate the embedding of tensor product algebras into the Leavitt algebra $L_{2,R}$. We show that the tensor product $L_{2,\mathbb{Z}}\otimes L_{2,\mathbb{Z}}$ does not embed in $L_{2,\mathbb{Z}}$ (as a uni
Externí odkaz:
http://arxiv.org/abs/1603.03618
Publikováno v:
Math. Ann., Vol. 369 (2017), no. 3-4, pp. 1061-1080
We show that the Cuntz splice induces stably isomorphic graph $C^*$-algebras.
Comment: Our arguments to prove invariance of the Cuntz splice for unital graph C*-algebras in arXiv:1505.06773 applied with only minor changes in the general case. Si
Comment: Our arguments to prove invariance of the Cuntz splice for unital graph C*-algebras in arXiv:1505.06773 applied with only minor changes in the general case. Si
Externí odkaz:
http://arxiv.org/abs/1602.03709
Autor:
Johansen, Rune, Sørensen, Adam P. W.
We show that the Leavitt path algebras $L_{2,\mathbb{Z}}$ and $L_{2-,\mathbb{Z}}$ are not isomorphic as $*$-algebras. There are two key ingredients in the proof. One is a partial algebraic translation of Matsumoto and Matui's result on diagonal prese
Externí odkaz:
http://arxiv.org/abs/1507.01247
We generalize the classification result of Restorff on Cuntz-Krieger algebras to cover all unital graph C*-algebras with real rank zero, showing that Morita equivalence in this case is determined by ordered, filtered K-theory as conjectured by three
Externí odkaz:
http://arxiv.org/abs/1505.06773
Autor:
Brownlowe, Nathan, Sørensen, Adam P W
Publikováno v:
Journal of Algebra, Volume 454, 15 May 2016, Pages 334-356
For a commutative ring $R$ with unit we show that the Leavitt path algebra $L_R(E)$ of a graph $E$ embeds into $L_{2,R}$ precisely when $E$ is countable. Before proving this result we prove a generalised Cuntz-Krieger Uniqueness Theorem for Leavitt p
Externí odkaz:
http://arxiv.org/abs/1503.08705