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作者：Peterson, Jesse; Thom, Andreas
作者单位：Leipzig University; Vanderbilt University
摘要：In this article we study cocycles of discrete countable groups with values in l(2)G and the ring of affiliated operators UG. We clarify properties of the first cohomology of a group G with coefficients in l(2)G and answer several questions from De Cornulier et al. (Transform. Groups 13(1): 125-147, 2008). Moreover, we obtain strong results about the existence of free subgroups and the subgroup structure, provided the group has a positive first l(2)-Betti number. We give numerous applications a...
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作者：Meyerovitch, Tom
摘要：We discuss some numerical invariants of multidimensional shifts of finite type (SFTs) which are associated with the growth rates of the number of admissible finite configurations. Extending an unpublished example of Tsirelson (A strange two-dimensional symbolic system, 1992), we show that growth complexities of the form exp (n (alpha+o(1))) are possible for non-integer alpha's. In terminology of de Carvalho (Port. Math. 54(1):19-40, 1997), such subshifts have entropy dimension alpha. The class...
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作者：Navarro, Gabriel; Tiep, Pham Huu
作者单位：University of Arizona; University of Valencia
摘要：The Alperin Weight Conjecture was stated by J. Alperin in 1986 and constitutes one of the main problems in the representation theory of finite groups. In this paper, we provide a reduction to simple groups and as an application we prove the conjecture in several cases.
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作者：Chen, Jungkai Alfred; Hacon, Christopher D.
作者单位：Utah System of Higher Education; University of Utah; National Taiwan University
摘要：Let f:X -> Y be an algebraic fiber space with general fiber F. If Y is of maximal Albanese dimension, we show that kappa(X)a parts per thousand yen kappa(Y)+kappa(F).
