A natural invariant algebra for the Baby Monster group

2007 ◽  
Vol 10 (1) ◽  
Author(s):  
Alexander J. E Ryba
Keyword(s):  
Invariant Algebra ◽  
Monster Group

scholarly journals The intersection graph of a finite simple group has diameter at most 5

2021 ◽  
Author(s):  
Saul D. Freedman
Keyword(s):  
Simple Group ◽  
Upper Bound ◽  
Finite Simple Group ◽  
Unitary Groups ◽  
Intersection Graph ◽  
Monster Group ◽  
Prime Dimension

AbstractLet G be a non-abelian finite simple group. In addition, let $$\Delta _G$$ Δ G be the intersection graph of G, whose vertices are the proper non-trivial subgroups of G, with distinct subgroups joined by an edge if and only if they intersect non-trivially. We prove that the diameter of $$\Delta _G$$ Δ G has a tight upper bound of 5, thereby resolving a question posed by Shen (Czechoslov Math J 60(4):945–950, 2010). Furthermore, a diameter of 5 is achieved only by the baby monster group and certain unitary groups of odd prime dimension.

scholarly journals On Certain Equations to the Cubic Surface, with Extensions to Higher Space

1934 ◽  
Vol 4 (1) ◽  
pp. 1-11
Author(s):  
W. Saddler
Keyword(s):  
The Other ◽  
Cubic Surface ◽  
Invariant Algebra ◽  
Quadric Cone

The Cubic Surface, as is well known, can be formulated as the locus of a point which, when joined to six given lines—one of which cuts the other five—forms planes enveloping a quadric cone.1 It might be of some interest to show how such a definition leads to one or two of the better known forms of the equation to the surface. The method of approach is by means of the Clebsch Transformation Principle in Geometry and the use of general coordinates. In particular, compound symbols and bracket factors, as developed by H. W. Turnbull2 in his works on Geometry and Invariant Algebra, have been largely used.

scholarly journals On the Action of the Sporadic Simple Baby Monster Group on its Conjugacy Class 2B

2008 ◽  
Vol 11 ◽  
pp. 15-27 ◽  
Author(s):  
Jürgen Müller
Keyword(s):  
Conjugacy Class ◽  
Maximal Subgroup ◽  
Endomorphism Ring ◽  
Free Action ◽  
Character Table ◽  
Computational Technique ◽  
Permutation Module ◽  
Monster Group ◽  
Multiplicity Free

AbstractWe determine the character table of the endomorphism ring of the permutation module associated with the multiplicity-free action of the sporadic simple Baby Monster group B on its conjugacy class 2B, where the centraliser of a 2B-element is a maximal subgroup of shape 21+22.Co2. This is one of the first applications of a new general computational technique to enumerate big orbits.

scholarly journals UNIVERSAL NEAR-HORIZON CONFORMAL STRUCTURE AND BLACK HOLE ENTROPY

2008 ◽  
Vol 23 (16n17) ◽  
pp. 2547-2561 ◽  
Author(s):  
SAYAN K. CHAKRABARTI ◽  
KUMAR S. GUPTA ◽  
SIDDHARTHA SEN
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Wide Class ◽  
Central Charge ◽  
Recent Observation ◽  
Algebraic Approach ◽  
Conformal Structure ◽  
Quantization Condition ◽  
Massless Scalar ◽  
Monster Group

It is shown that a massless scalar probe reveals a universal near-horizon conformal structure for a wide class of black holes, including the BTZ. The central charge of the corresponding Virasoro algebra contains information about the black hole. With a suitable quantization condition on the central charge, the CFT associated with the black hole in our approach is consistent with the recent observation of Witten, where the dual theory for the BTZ in the AdS/CFT framework has been identified with the construction of Frenkel, Lepowsky and Meurman. This CFT admits the Fischer–Griess monster group as its symmetry. The logarithm of the dimension of a specific representation of the monster group has been identified by Witten as the entropy of the BTZ black hole. Our algebraic approach shows that a wide class of black holes share the same near-horizon conformal structure as that for the BTZ. With a suitable quantization condition, the CFT's for all these black holes in our formalism can be identified with the FLM model, although not through the AdS/CFT correspondence. The corresponding entropy for the BTZ provides a lower bound for the entropy of this entire class of black holes.

Differential Invariants of the (2+1)-Dimensional Breaking Soliton Equation

2016 ◽  
Vol 71 (9) ◽  
pp. 855-862
Author(s):  
Zhong Han ◽  
Yong Chen
Keyword(s):  
Recurrence Relations ◽  
Differential Invariant ◽  
Lie Symmetry ◽  
Differential Invariants ◽  
Moving Frame ◽  
Moving Frames ◽  
Soliton Equation ◽  
Invariant Algebra ◽  
Equivariant Moving Frames

AbstractWe construct the differential invariants of Lie symmetry pseudogroups of the (2+1)-dimensional breaking soliton equation and analyze the structure of the induced differential invariant algebra. Their syzygies and recurrence relations are classified. In addition, a moving frame and the invariantization of the breaking soliton equation are also presented. The algorithms are based on the method of equivariant moving frames.

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