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Relevant bibliographies by topics / Twisted semigroup algebra

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Journal articles
Dissertations / Theses
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Academic literature on the topic 'Twisted semigroup algebra'

Author: Grafiati

Published: 4 June 2021

Last updated: 20 February 2023

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Journal articles on the topic "Twisted semigroup algebra"

1

Guo, Xiaojiang, and Changchang Xi. "Cellularity of twisted semigroup algebras." Journal of Pure and Applied Algebra 213, no. 1 (January 2009): 71–86. http://dx.doi.org/10.1016/j.jpaa.2008.05.004.

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2

Laca, Marcelo. "Discrete product systems with twisted units." Bulletin of the Australian Mathematical Society 52, no. 2 (October 1995): 317–26. http://dx.doi.org/10.1017/s000497270001474x.

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The spectral C*-algebra of the discrete product systems of H.T. Dinh is shown to be a twisted semigroup crossed product whenever the product system has a twisted unit. The covariant representations of the corresponding dynamical system are always faithful, implying the simplicity of these crossed products; an application of a recent theorem of G.J. Murphy gives their nuclearity. Furthermore, a semigroup of endomorphisms of B(H) having an intertwining projective semigroup of isometries can be extended to a group of automorphisms of a larger Type I factor.

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3

Wilcox, Stewart. "Cellularity of diagram algebras as twisted semigroup algebras." Journal of Algebra 309, no. 1 (March 2007): 10–31. http://dx.doi.org/10.1016/j.jalgebra.2006.10.016.

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Chang, Gyu Whan, and Dong Yeol Oh. "Divisibility properties of twisted semigroup rings." Communications in Algebra 48, no. 3 (October 20, 2019): 1191–200. http://dx.doi.org/10.1080/00927872.2019.1677693.

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5

Klep, Igor. "On Valuations, Places and Graded Rings Associated to ∗-Orderings." Canadian Mathematical Bulletin 50, no. 1 (March 1, 2007): 105–12. http://dx.doi.org/10.4153/cmb-2007-010-4.

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AbstractWe study natural ∗-valuations, ∗-places and graded ∗-rings associated with ∗-ordered rings. We prove that the natural ∗-valuation is always quasi-Ore and is even quasi-commutative (i.e., the corresponding graded ∗-ring is commutative), provided the ring contains an imaginary unit. Furthermore, it is proved that the graded ∗-ring is isomorphic to a twisted semigroup algebra. Our results are applied to answer a question of Cimprič regarding ∗-orderability of quantum groups.

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Rigal, L., and P. Zadunaisky. "Twisted Semigroup Algebras." Algebras and Representation Theory 18, no. 5 (August 7, 2015): 1155–86. http://dx.doi.org/10.1007/s10468-015-9525-z.

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Adji, Sriwulan, and Rizky Rosjanuardi. "Twisted Semigroup Crossed Products and Twisted Toeplitz Algebras of Ordered Groups." Acta Mathematica Sinica, English Series 23, no. 9 (December 12, 2006): 1639–48. http://dx.doi.org/10.1007/s10114-005-0907-8.

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8

Phillips, John, and Iain Raeburn. "Semigroups of isometries, Toeplitz algebras and twisted crossed products." Integral Equations and Operator Theory 17, no. 4 (December 1993): 579–602. http://dx.doi.org/10.1007/bf01200396.

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9

East, James. "Presentations for Temperley–Lieb Algebras." Quarterly Journal of Mathematics, February 22, 2021. http://dx.doi.org/10.1093/qmath/haab001.

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Abstract We give a new and conceptually straightforward proof of the well-known presentation for the Temperley–Lieb algebra, via an alternative new presentation. Our method involves twisted semigroup algebras, and we make use of two apparently new submonoids of the Temperley–Lieb monoid.

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10

STEINBERG, BENJAMIN. "TWISTS, CROSSED PRODUCTS AND INVERSE SEMIGROUP COHOMOLOGY." Journal of the Australian Mathematical Society, October 8, 2021, 1–36. http://dx.doi.org/10.1017/s144678872100015x.

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Abstract Twisted étale groupoid algebras have recently been studied in the algebraic setting by several authors in connection with an abstract theory of Cartan pairs of rings. In this paper we show that extensions of ample groupoids correspond in a precise manner to extensions of Boolean inverse semigroups. In particular, discrete twists over ample groupoids correspond to certain abelian extensions of Boolean inverse semigroups, and we show that they are classified by Lausch’s second cohomology group of an inverse semigroup. The cohomology group structure corresponds to the Baer sum operation on twists. We also define a novel notion of inverse semigroup crossed product, generalizing skew inverse semigroup rings, and prove that twisted Steinberg algebras of Hausdorff ample groupoids are instances of inverse semigroup crossed products. The cocycle defining the crossed product is the same cocycle that classifies the twist in Lausch cohomology.

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Dissertations / Theses on the topic "Twisted semigroup algebra"

1

Wilcox, Stewart. "Cellularity of Twisted Semigroup Algebras of Regular Semigroups." Thesis, The University of Sydney, 2005. http://hdl.handle.net/2123/720.

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There has been much interest in algebras which have a basis consisting of diagrams, which are multiplied in some natural diagrammatic way. Examples of these so-called diagram algebras include the partition, Brauer and Temperley-Lieb algebras. These three examples all have the property that the product of two diagram basis elements is always a scalar multiple of another basis element. Motivated by this observation, we find that these algebras are examples of twisted semigroup algebras. Such algebras are an obvious extension of twisted group algebras, which arise naturally in various contexts; examples include the complex numbers and the quaternions, considered as algebras over the real numbers. The concept of a cellular algebra was introduced in a famous paper of Graham and Lehrer; an algebra is called cellular if it has a basis of a certain form, in which case the general theory of cellular algebras allows us to easily derive information about the semisimplicity of the algebra and about its representation theory, even in the non-semisimple case. Many diagram algebras (including the above three examples) are known to be cellular. The aim of this thesis is to deduce the cellularity of these examples (and others) by proving a general result about the cellularity of twisted semigroup algebras. This will extend a recent result of East. In Chapters 2 and 3 we discuss semigroup theory and twisted semigroup algebras, and realise the above three examples as twisted semigroup algebras. Chapters 4 to 7 detail and extend slightly the theory of cellular algebras. In Chapter 8 we state and prove the main theorem, which shows that certain twisted semigroup algebras are cellular. Under the assumptions of the main theorem, we explore the cell representations of twisted semigroup algebras in Chapter 9. Finally in Chapter 10, we apply the theorem to various examples, including the three diagram algebras mentioned above.

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2

Wilcox, Stewart. "Cellularity of Twisted Semigroup Algebras of Regular Semigroups." University of Sydney. Mathematics and Statistics, 2006. http://hdl.handle.net/2123/720.

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Abstract:

There has been much interest in algebras which have a basis consisting of diagrams, which are multiplied in some natural diagrammatic way. Examples of these so-called diagram algebras include the partition, Brauer and Temperley-Lieb algebras. These three examples all have the property that the product of two diagram basis elements is always a scalar multiple of another basis element. Motivated by this observation, we find that these algebras are examples of twisted semigroup algebras. Such algebras are an obvious extension of twisted group algebras, which arise naturally in various contexts; examples include the complex numbers and the quaternions, considered as algebras over the real numbers. The concept of a cellular algebra was introduced in a famous paper of Graham and Lehrer; an algebra is called cellular if it has a basis of a certain form, in which case the general theory of cellular algebras allows us to easily derive information about the semisimplicity of the algebra and about its representation theory, even in the non-semisimple case. Many diagram algebras (including the above three examples) are known to be cellular. The aim of this thesis is to deduce the cellularity of these examples (and others) by proving a general result about the cellularity of twisted semigroup algebras. This will extend a recent result of East. In Chapters 2 and 3 we discuss semigroup theory and twisted semigroup algebras, and realise the above three examples as twisted semigroup algebras. Chapters 4 to 7 detail and extend slightly the theory of cellular algebras. In Chapter 8 we state and prove the main theorem, which shows that certain twisted semigroup algebras are cellular. Under the assumptions of the main theorem, we explore the cell representations of twisted semigroup algebras in Chapter 9. Finally in Chapter 10, we apply the theorem to various examples, including the three diagram algebras mentioned above.

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3

Wilcox, Stewart. "Cellularity of twisted semigroup algebras of regular semigroups /." Connect to full text, 2005. http://hdl.handle.net/2123/720.

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Book chapters on the topic "Twisted semigroup algebra"

1

Karpilovsky, G. "Blocks and Vertices of Twisted Group Algebras." In Group and Semigroup Rings, Centro de Brasileiro de Pesquisas Fisicas Rio de Janeiro and University of Rochester, 91–97. Elsevier, 1986. http://dx.doi.org/10.1016/s0304-0208(08)71514-7.

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2

Karpilovsky, G. "Extending Indecomposable Modules Over Twisted Group Algebras." In Group and Semigroup Rings, Centro de Brasileiro de Pesquisas Fisicas Rio de Janeiro and University of Rochester, 109–16. Elsevier, 1986. http://dx.doi.org/10.1016/s0304-0208(08)71516-0.

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Karpilovsky, G. "Defect Groups of Blocks of Twisted Group Algebras." In Group and Semigroup Rings, Centro de Brasileiro de Pesquisas Fisicas Rio de Janeiro and University of Rochester, 99–108. Elsevier, 1986. http://dx.doi.org/10.1016/s0304-0208(08)71515-9.

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