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Page 7059 of Mathematical Reviews Vol. , Issue 2002J [page]

2002 Mathematical Reviews  
The author obtains a classification of infinite algebras with k-transitive groups of weak automorphisms for k > 3. Andrei A.  ...  The paper continues the author’s investigation of algebras with large groups of automorphisms and weak automorphisms [see, e.g., Acta Sci. Math.  ... 

A new trichotomy theorem for groups of finite Morley rank

Alexandre Borovik, Jeffrey Burdges
2007 Journal of the London Mathematical Society  
There is a longstanding conjecture, due to Gregory Cherlin and Boris Zilber, that all simple groups of finite Morley rank are simple algebraic groups.  ...  Here we will conclude that a simple K * -group of finite Morley rank and odd type has normal rank at most two.  ...  Given an algebraic group G, a maximal torus T of G, and a Borel subgroup B of G which contains T , we define the group Γ of graph automorphisms associated to T and B, to be the group of algebraic automorphisms  ... 
doi:10.1112/jlms/jdm088 fatcat:ttpd3nspx5cw3muormnuzlraky

On small world non-Sunada twins and cellular Voronoi diagrams

V. Ustimenko, Institute of Mathematics Maria Curie-Skłdowska University, Institute of Telecommunications and Global Information Space NAS of Ukraine
2020 Algebra and discrete mathematics  
Two families of small world graphs Gi and Hi form a family of non-Sunada twins if Gi and Hi are isospectral of bounded diameter but groups Aut(Gi) and Aut(Hi) are nonisomorphic.  ...  Two new families of distance-regular—but not distance-transitive—graphs will be introduced.  ...  If J = {n} then the graphs C J (n, q) and B J (n, q) form a balanced family of small world non-Sunada twins with respective automorphism groups N (C n (q)) and N (D n+1 (q)). J.  ... 
doi:10.12958/adm1343 fatcat:p7bsw2lbzrgehl3yq5vzlejzry

Page 5294 of Mathematical Reviews Vol. , Issue 93j [page]

1993 Mathematical Reviews  
Then, for every finite group I, there exists a graph G € F(H) such that the automorphism group of G is isomorphic to I.  ...  Summary: “Leland and Solomon introduced a family of trivalent graphs, called Mobius graphs, and because of their small diameter suggested that they be used as an effective interconnection scheme for multiprocessor  ... 

A New Trichotomy Theorem [article]

Alexandre Borovik, Jeffrey Burdges
2007 arXiv   pre-print
We show that a minimal counter example to the Cherlin-Zilber Algebraicity Conjecture for simple groups of finite Morley rank has normal 2-rank at most two, which is a tameness free version of Borovik's  ...  This result serves as a bridge by showing that there are no groups found strictly between the generic and quasithin cases, i.e. between groups of Lie rank at least three, and groups of Lie rank one and  ...  Given an algebraic group G, a maximal torus T of G, and a Borel subgroup B of G which contains T , we define the group Γ of graph automorphisms associated to T and B, to be the group of algebraic automorphisms  ... 
arXiv:0711.4169v1 fatcat:wmee46f4uzeyjf6eea5x47hqge

On the key exchange with new cubical maps based on graphs

Urszula Romańczuk, Vasyl Ustimenko
2011 Annales UMCS Informatica  
Families of edge transitive algebraic graphs Fn(K), over the commutative ring K were used for the graph based cryptographic algorithms.  ...  There is a well defined projective limit lim A(n, K) = A(K), n → ∞ which is an infinite bipatrtite graph with point set P = lim Pn and line set L = limLn.  ...  The graph A(n, K) is the triangular algebraic graph over the commutative ring K. This family was defined in [2, 16, 17] .  ... 
doi:10.2478/v10065-011-0038-z fatcat:l25levhyhrfxhhqg4if22aggvi

Graphs from Generalized Kac--Moody Algebras

T. Arthur Terlep, Jason Williford
2012 SIAM Journal on Discrete Mathematics  
In this paper, we construct new families of graphs whose automorphism groups are transitive on 3-paths.  ...  We will show that one particular subfamily gives new lower bounds on the number of edges in extremal graphs with no cycles of length fourteen.  ...  This paper was motivated by trying to find a Lie algebra which gives D(k, q) and graphs for all generalized Cartan matrices. We thank Woldar for all his encouragement in this endeavor.  ... 
doi:10.1137/11085298x fatcat:nxblcu5y3jb7xg34g5b4g4vecq

Page 1242 of Mathematical Reviews Vol. 36, Issue 6 [page]

1968 Mathematical Reviews  
graphs. | fractions are defined, and the calculus of left fractions is discussed.  ...  Theorem : Let G be an abelian group of automorphisms of /. Let € be a Cartan subalge- bra of #,(@).  ... 

Automorphisms of the bipartite graph planar algebra

R.D. Burstein
2010 Journal of Functional Analysis  
In this paper, we classify the automorphism group of a bipartite graph planar algebra, and obtain subfactor planar subalgebras by taking fixed points under groups of automorphisms.  ...  This construction provides both new examples of subfactors and new descriptions of the planar algebras of previously known examples.  ...  In this paper, we describe a method for doing so by taking fixed points of a BGPA under a group of automorphisms. In Section 2 we describe BGPAs, with particular attention to infinite graphs.  ... 
doi:10.1016/j.jfa.2010.05.009 fatcat:3lyata5munc37gtphogkdkm56u

Page 2415 of Mathematical Reviews Vol. , Issue 2003d [page]

2003 Mathematical Reviews  
In the present article the author obtains explicit equations of a new family of algebraic curves defining Riemann surfaces with trivial automorphism group.  ...  The paper reviews these well-known facts and constructs a graph describing the above action of the braid group on quadruples. This graph is called a megamap. A few small examples are given.  ... 

Exotic automorphisms of the Schouten algebra of polyvector fields [article]

S.A. Merkulov
2010 arXiv   pre-print
Using a new compactification of the (braid) configuration space of n points in the upper half plane we construct a family of exotic Lie-infinity automorphisms of the Schouten algebra of polyvector fields  ...  on an affine space depending on a Kontsevich type propagator.  ...  Exotic automorphisms of the Schouten algebra of polyvector fields  ... 
arXiv:0809.2385v6 fatcat:f2ngxdvrlvepxdbbjpzrekfg64

Automorphisms of the bipartite graph planar algebra [article]

R.D. Burstein
2010 arXiv   pre-print
In this paper, we classify the automorphism group of a bipartite graph planar algebra, and obtain subfactor planar subalgebras by taking fixed points under groups of automorphisms.  ...  This construction provides both new examples of subfactors and new descriptions of the planar algebras of previously known examples.  ...  For finite graphs with the correct spin vector, any sufficiently small planar subalgebra is of subfactor type. Lemma 4.1. Let P Γ be a bipartite graph planar algebra with spin vector µ.  ... 
arXiv:1003.2676v1 fatcat:wwofsusfsbc2niphuf3d4i2dle

Automorphism groups of saturated structures; a review [article]

Daniel Lascar
2003 arXiv   pre-print
The main themes are: the small index property in the countable and uncountable cases; the possibility of recovering a structure or a significant part of it from its automorphism group; the subgroup of  ...  We will review the main results concerning the automorphism groups of saturated structures which were obtained during the two last decades.  ...  By definition, a subset X of M n /E is closed if and only if ϕ −1 E (X) is the intersection of a family of subsets definable with parameters.  ... 
arXiv:math/0304205v1 fatcat:ujxgfuz7ubcu5mi5hsnzxrbt6y

Page 48 of Mathematical Reviews Vol. , Issue 2002A [page]

2002 Mathematical Reviews  
Such a family generates a point-regular linear space, i.e. a linear space with an automorphism group acting regularly on the point-set.  ...  The authors construct a new family of strongly regular (but not Paley) 3-e.c. graphs Che construction is based on the existence of certain Hadamard matrices Arne Winterhof (A-OAW-DM,;; Vienna 2002a:05053  ... 

Automorphism covariant representations of the holonomy-flux lowast-algebra

Andrzej Okołów, Jerzy Lewandowski
2005 Classical and quantum gravity  
We define the automorphism covariance of a *-representation of the algebra on a Hilbert space and prove that the only Hilbert space admitting such a representation is a direct sum of spaces L^2 given by  ...  We consider an arbitrary principal bundle of a compact connected structure group and following Sahlmann's ideas define a holonomy-flux *-algebra whose elements correspond to the elementary variables.  ...  Woronowicz encouraged us to reformulate our results in the language of non-trivial principal bundles. We are grateful to Marcin Bobieński for a discussion which helped us to formulate Lemma 6.2.  ... 
doi:10.1088/0264-9381/22/4/002 fatcat:5wiyev3xpfhljfa32ezeambit4
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