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23
FUNDAMENTAL SEMIGROUPS HAVING A BAND OF IDEMPOTENTS
, 2007
"... The construction by Hall of a fundamental orthodox semigroup WB from a band B provides an important tool in the study of orthodox semigroups. We present here a semigroup SB that plays the role of WB for a class of semigroups having a band of idempotents B. Specifically, the semigroups we consider a ..."
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The construction by Hall of a fundamental orthodox semigroup WB from a band B provides an important tool in the study of orthodox semigroups. We present here a semigroup SB that plays the role of WB for a class of semigroups having a band of idempotents B. Specifically, the semigroups we consider
A conjecture on the Hall topology for the free group
, 1991
"... The Hall topology for the free group is the coarsest topology such that every group morphism from the free group onto a finite discrete group is continuous. It was shown by M. Hall Jr that every finitely generated subgroup of the free group is closed for this topology. We conjecture that if H1 ; H2 ..."
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Cited by 31 (5 self)
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The Hall topology for the free group is the coarsest topology such that every group morphism from the free group onto a finite discrete group is continuous. It was shown by M. Hall Jr that every finitely generated subgroup of the free group is closed for this topology. We conjecture that if H1 ; H2
Representations of Hecke algebras and dilations of semigroup crossed products
 J. London Math. Soc
, 2002
"... Abstract. We consider a family of Hecke C ∗algebras which can be realised as crossed products by semigroups of endomorphisms. We show by dilating representations of the semigroup crossed product that the category of representations of the Hecke algebra is equivalent to the category of continuous un ..."
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Cited by 8 (4 self)
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classes of C∗Hecke algebras which can be realised as semigroup crossed products [13, 1, 3, 11], and these realisations have provided valuable insight to the work of Bost and Connes [9, 18]. A recent theorem of Hall [5] asserts that, for a large class of Hecke pairs (Γ, M), the category of nondegenerate
BassSerre Theory for Groupoids and the Structure of Full Regular Semigroup Amalgams
 Ž. JOURNAL OF ALGEBRA 183, 38�54 1996 ARTICLE NO. 0206
, 1996
"... T. E. Hall proved in 1978 that if �S, S; U � 1 2 is an amalgam of regular semigroups in which S � S � U is a full regular subsemigroup of S and S Ž 1 2 1 2 i.e., S 1, S 2, and U have the same set of idempotents., then the amalgam is strongly embeddable in a regular semigroup S that contains S 1, S 2 ..."
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Cited by 11 (3 self)
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T. E. Hall proved in 1978 that if �S, S; U � 1 2 is an amalgam of regular semigroups in which S � S � U is a full regular subsemigroup of S and S Ž 1 2 1 2 i.e., S 1, S 2, and U have the same set of idempotents., then the amalgam is strongly embeddable in a regular semigroup S that contains S 1
Duality in Multilayered Quantum Hall Systems
, 1992
"... The braid group dynamics captures the fractional quantum Hall effect (FQHE) as a manifestation of puncture phase. When the dynamics is generalized for particles on a multisheeted surface, we obtain new tools which determine the fractional charges, the quantum statistics, and the filling factors of ..."
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of the manybody system displaying FQHE: ψm = ∏ (wa − wb) m exp( − 1 4ℓ2 ∑ wa  2), (1) a<b where ℓ denotes the magnetic length and wa are the coordinates of N electrons. Now, this ansätz is for singlelayered quantum Hall system, with all the spins of the electrons polarized in the direction
Pulé: Propagating edge states for a magnetic Hamiltonian
, 1999
"... We study the quantum mechanical motion of a charged particle moving in a half plane (x> 0) subject to a uniform constant magnetic field B directed along the zaxis and to an arbitrary impurity potential WB, assumed to be weak in the sense that WB ∞ < δB, for some δ small enough. We show ri ..."
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Cited by 34 (0 self)
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rigorously a phenomenon pointed out by Halperin in his work on the quantum Hall effect, namely the existence of current carrying and extended edge states in such a situation. More precisely, we show that there exist states propagating with a speed of size B 1/2 in the ydirection, no matter how fast WB
Ash's type II theorem, profinite topology and Malcev products Part I
"... This paper is concerned with the many deep and far reaching consequences of Ash's positive solution of the type II conjecture for finite monoids. After rewieving the statement and history of the problem, we show how it can be used to decide if a finite monoid is in the variety generated by t ..."
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Cited by 47 (10 self)
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such that every element has at most one semigroup inverse. As a consequence of the cover conjecture  also verified by Ash  it follows that block groups are precisely the divisors of power monoids of finite groups. The proof of this last fact uses earlier results of the authors and the deepest tools
References
"... A probabilistic approach to analytic arithmetic on algebraic function fields. (English summary) Math. Proc. Cambridge Philos. Soc. 139 (2005), no. 1, 1–26. Summary: “J. Knopfmacher [Analytic arithmetic of algebraic function fields, Dekker, New York, 1979; MR0545904 (81d:10031)] introduced the idea o ..."
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of an additive arithmetic semigroup as a general setting for an algebraic analogue of number theory. Within his framework, W.B. Zhang [in
CLOSURES OF REGULAR LANGUAGES FOR PROFINITE TOPOLOGIES
"... Abstract. The PinReutenauer algorithm gives a method, that can be viewed as a descriptive procedure, to compute the closure in the free group of a regular language with respect to the Hall topology. A similar descriptive procedure is shown to hold for the pseudovariety A of aperiodic semigroups, w ..."
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Abstract. The PinReutenauer algorithm gives a method, that can be viewed as a descriptive procedure, to compute the closure in the free group of a regular language with respect to the Hall topology. A similar descriptive procedure is shown to hold for the pseudovariety A of aperiodic semigroups
Results 1  10
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23