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Relevant bibliographies by topics / Group theory. Linear algebraic groups. Piecewise linear topology

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Academic literature on the topic 'Group theory. Linear algebraic groups. Piecewise linear topology'

Author: Grafiati

Published: 4 June 2021

Last updated: 9 February 2022

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Journal articles on the topic "Group theory. Linear algebraic groups. Piecewise linear topology"

1

Wendt, Matthias. "Rationally trivial torsors in -homotopy theory." Journal of K-theory 7, no. 3 (2011): 541–72. http://dx.doi.org/10.1017/is011004020jkt157.

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AbstractIn this paper, we show that rationally trivial torsors under split smooth linear algebraic groups induce fibre sequences in -homotopy theory. The results allow geometric proofs of stabilization results for unstable Karoubi-Villamayor K-theories and a description of the second -homotopy group of the projective line.

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Christiansen, Snorre H., Hans Z. Munthe-Kaas, and Brynjulf Owren. "Topics in structure-preserving discretization." Acta Numerica 20 (April 28, 2011): 1–119. http://dx.doi.org/10.1017/s096249291100002x.

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In the last few decades the concepts of structure-preserving discretization, geometric integration and compatible discretizations have emerged as subfields in the numerical approximation of ordinary and partial differential equations. The article discusses certain selected topics within these areas; discretization techniques both in space and time are considered. Lie group integrators are discussed with particular focus on the application to partial differential equations, followed by a discussion of how time integrators can be designed to preserve first integrals in the differential equation

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Joseph, Michael. "Antichain Toggling and Rowmotion." Electronic Journal of Combinatorics 26, no. 1 (2019). http://dx.doi.org/10.37236/7454.

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In this paper, we analyze the toggle group on the set of antichains of a poset. Toggle groups, generated by simple involutions, were first introduced by Cameron and Fon-Der-Flaass for order ideals of posets. Recently Striker has motivated the study of toggle groups on general families of subsets, including antichains. This paper expands on this work by examining the relationship between the toggle groups of antichains and order ideals, constructing an explicit isomorphism between the two groups (for a finite poset). We also focus on the rowmotion action on antichains of a poset that has been w

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Chayet, Maurice, and Skip Garibaldi. "A class of continuous non-associative algebras arising from algebraic groups including." Forum of Mathematics, Sigma 9 (2021). http://dx.doi.org/10.1017/fms.2020.66.

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Abstract We give a construction that takes a simple linear algebraic group G over a field and produces a commutative, unital, and simple non-associative algebra A over that field. Two attractions of this construction are that (1) when G has type $E_8$ , the algebra A is obtained by adjoining a unit to the 3875-dimensional representation; and (2) it is effective, in that the product operation on A can be implemented on a computer. A description of the algebra in the $E_8$ case has been requested for some time, and interest has been increased by the recent proof that $E_8$ is the full automorphi

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McCourt, Thomas A. "Growth Rates of Groups associated with Face 2-Coloured Triangulations and Directed Eulerian Digraphs on the Sphere." Electronic Journal of Combinatorics 23, no. 1 (2016). http://dx.doi.org/10.37236/5410.

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Let $\mathcal{G}$ be a properly face $2$-coloured (say black and white) piecewise-linear triangulation of the sphere with vertex set $V$. Consider the abelian group $\mathcal{A}_W$ generated by the set $V$, with relations $r+c+s=0$ for all white triangles with vertices $r$, $c$ and $s$. The group $\mathcal{A}_B$ can be defined similarly, using black triangles. These groups are related in the following manner $\mathcal{A}_W\cong\mathcal{A}_B\cong\mathbb{Z}\oplus\mathbb{Z}\oplus\mathcal{C}$ where $\mathcal{C}$ is a finite abelian group.The finite torsion subgroup $\mathcal{C}$ is referred to as

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6

FRESSE, LUCAS, and IVAN PENKOV. "MULTIPLE FLAG IND-VARIETIES WITH FINITELY MANY ORBITS." Transformation Groups, May 1, 2021. http://dx.doi.org/10.1007/s00031-021-09653-0.

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AbstractLet G be one of the ind-groups GL(∞), O(∞), Sp(∞), and let P1, ..., Pℓ be an arbitrary set of ℓ splitting parabolic subgroups of G. We determine all such sets with the property that G acts with finitely many orbits on the ind-variety X1 × × Xℓ where Xi = G/Pi. In the case of a finite-dimensional classical linear algebraic group G, the analogous problem has been solved in a sequence of papers of Littelmann, Magyar–Weyman–Zelevinsky and Matsuki. An essential difference from the finite-dimensional case is that already for ℓ = 2, the condition that G acts on X1 × X2 with finitely many orbi

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Dissertations / Theses on the topic "Group theory. Linear algebraic groups. Piecewise linear topology"

1

Housley, Matthew L. "Conjugacy Classes of the Piecewise Linear Group." Diss., CLICK HERE for online access, 2006. http://contentdm.lib.byu.edu/ETD/image/etd1442.pdf.

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Books on the topic "Group theory. Linear algebraic groups. Piecewise linear topology"

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Borel, Armand. Continuous cohomology, discrete subgroups, and representations of reductive groups. 2nd ed. American Mathematical Society, 2000.

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1975-, Champanerkar Abhijit, ed. Interactions between hyperbolic geometry, quantum topology, and number theory: Workshop, June 3-13, 2009, conference, June 15-19, 2009, Columbia University, New ork, NY. American Mathematical Society, 2011.

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Topology and geometry in dimension three: Triangulations, invariants, and geometric structures : conference in honor of William Jaco's 70th birthday, June 4-6, 2010, Oklahoma State University, Stillwater, OK. American Mathematical Society, 2011.

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Tensor categories. American Mathematical Society, 2015.

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1980-, Blazquez-Sanz David, Morales Ruiz, Juan J. (Juan José), 1953-, and Lombardero Jesus Rodriguez 1961-, eds. Symmetries and related topics in differential and difference equations: Jairo Charris Seminar 2009, Escuela de Matematicas, Universidad Sergio Arboleda, Bogotá, Colombia. American Mathematical Society, 2011.

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Wallach, Nolan R., and Armand Borel. Continuous Cohomology, Discrete Subgroups, and Representations of Reductivegroups (Annals of Mathematics Studies (Paperback)). Princeton University Press, 2001.

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