@misc{10498/16102, year = {2014}, month = {1}, url = {http://hdl.handle.net/10498/16102}, abstract = {We study the crossed product C⁎C⁎-algebra associated to injective endomorphisms, which turns out to be equivalent to study the crossed product by the dilated automorphism. We prove that the dilation of the Bernoulli p -shift endomorphism is topologically free. As a consequence, we have a way to twist any endomorphism of a DD-absorbing C⁎C⁎-algebra into one whose dilated automorphism is essentially free and have the same K -theory map than the original one. This allows us to construct purely infinite crossed products C⁎C⁎-algebras with diverse ideal structures.}, keywords = {Crossed product}, keywords = {Dilation}, keywords = {Shift endomorphism}, keywords = {Rokhlin property}, keywords = {Purely infinite}, title = {Purely infinite crossed products by endomorphisms}, doi = {10.1016/j.jmaa.2013.10.078}, author = {Ortega, E. and Pardo Espino, Enrique}, }