On local weak crossed product orders

2014 ◽  
Vol 135 (1) ◽  
pp. 53-68 ◽  
Author(s):  
Th. Theohari-Apostolidi ◽  
A. Tompoulidou
Keyword(s):  
Crossed Product ◽  
Weak Crossed Product

Constructing the hereditary crossed product order containing a given weak crossed product order and a criterion for weakness

2016 ◽  
Vol 15 (06) ◽  
pp. 1650113
Author(s):  
Christopher James Wilson
Keyword(s):  
Galois Extension ◽  
Valuation Ring ◽  
Discrete Valuation Ring ◽  
Integral Closure ◽  
Crossed Product ◽  
Weak Crossed Product ◽  
Product Order

Consider a weak crossed product order [Formula: see text] in [Formula: see text], where [Formula: see text] is the integral closure of a discrete valuation ring [Formula: see text] in a tamely ramified Galois extension [Formula: see text] of the field of fractions of [Formula: see text]. Assume that [Formula: see text] is local. In this paper, we show that [Formula: see text] is hereditary if and only if it is maximal among the weak crossed product orders in [Formula: see text]. We also give an algorithm that constructs, in terms of the basis elements [Formula: see text] and the cocycle [Formula: see text], the unique hereditary weak crossed product order in [Formula: see text] that contains a given [Formula: see text], and we give a criterion for determining whether that hereditary order will have a cocycle that takes nonunit values in [Formula: see text].

scholarly journals Comparison of two notions of weak crossed product

2020 ◽  
pp. 2150059
Author(s):  
Jorge A. Guccione ◽  
Juan J. Guccione
Keyword(s):  
Hopf Algebra ◽  
Hopf Algebras ◽  
Crossed Product ◽  
Weak Hopf Algebra ◽  
Crossed Products ◽  
Hopf Algebroid ◽  
Hopf Algebroids ◽  
Weak Crossed Product ◽  
Cleft Extensions ◽  
Weak Hopf Algebras

We compare the restriction to the context of weak Hopf algebras of the notion of crossed product with a Hopf algebroid introduced in [Cleft extensions of Hopf algebroids, Appl. Categor. Struct. 14(5–6) (2006) 431–469] with the notion of crossed product with a weak Hopf algebra introduced in [Crossed products for weak Hopf algebras with coalgebra splitting, J. Algebra 281(2) (2004) 731–752].

ON THE REPRESENTATIONS OF WEAK CROSSED PRODUCTS

2012 ◽  
Vol 11 (04) ◽  
pp. 1250169
Author(s):  
BING-LIANG SHEN ◽  
BAO-LIN XIONG
Keyword(s):  
Hopf Algebras ◽  
Projective Dimension ◽  
Crossed Product ◽  
Weak Hopf Algebra ◽  
Closed Field ◽  
Representation Dimension ◽  
Gorenstein Algebra ◽  
Finite Dimensional ◽  
Crossed Product Algebra ◽  
Weak Crossed Product

Let H be a finite-dimensional weak Hopf algebra in the sense of [G. Böhm and K. Szlachányi, A coassociative C*-quantum group with nonintegral dimensions, Lett. Math. Phys.35 (1996) 437–456] which is semisimple as well as its dual H*, A be a finite-dimensional algebra measured by H and A#σH be a weak crossed product. Then we first prove that the representation dimension of A#σH equals to that of A. Moreover, we will show that over an algebraically closed field k, the representation type between A and its weak crossed product algebra A#σH is coincident, which extends the result given by Liu [On the structure of tame graded basic Hopf algebras, J. Algebra 299 (2006) 841–853]. Finally, we show that A#σH is a CM-finite n-Gorenstein algebra if and only if so is A and the global Gorenstein projective dimension of A#σH is equal to that of A.

scholarly journals The Dixmier-Douady class of groupoid crossed products

2004 ◽  
Vol 76 (2) ◽  
pp. 223-234 ◽  
Author(s):  
Paul S. Muhly ◽  
Dana P. Williams
Keyword(s):  
Crossed Product ◽  
Crossed Products ◽  
Continuous Trace

AbstractWe give a formula for the Dixmier-Douady class of a continuous-trace groupoid crossed product that arises from an action of a locally trivial, proper, principal groupoid on a bundle of elementary C*-algebras that satisfies Fell's condition.

scholarly journals Classifying crossed product C*-algebras

2016 ◽  
Vol 138 (3) ◽  
pp. 793-820 ◽  
Author(s):  
Wilhelm Winter
Keyword(s):  
Crossed Product ◽  
C Algebras
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