The principal block idempotent

1991 ◽  
Vol 56 (4) ◽  
pp. 313-319 ◽  
Author(s):  
Burkhard K�lshammer
Keyword(s):  
Principal Block ◽  
Block Idempotent

scholarly journals Extension Quiver for Lie Superalgebra q(3)

2020 ◽  
Author(s):  
Nikolay Grantcharov ◽  
◽  
Vera Serganova ◽  
Keyword(s):  
Lie Superalgebra ◽  
Principal Block ◽  
Finite Dimensional ◽  
Standard Block ◽  
Projective Covers

We describe all blocks of the category of finite-dimensional q(3)-supermodules by providing their extension quivers. We also obtain two general results about the representation of q(n): we show that the Ext quiver of the standard block of q(n) is obtained from the principal block of q(n-1) by identifying certain vertices of the quiver and prove a virtual BGG-reciprocity for q(n). The latter result is used to compute the radical filtrations of q(3) projective covers.

scholarly journals SIMPLE MODULES IN THE AUSLANDER–REITEN QUIVER OF PRINCIPAL BLOCKS WITH ABELIAN DEFECT GROUPS

2018 ◽  
Vol 235 ◽  
pp. 58-85
Author(s):  
SHIGEO KOSHITANI ◽  
CAROLINE LASSUEUR
Keyword(s):  
Finite Group ◽  
Simple Groups ◽  
Finite Simple Groups ◽  
Simple Modules ◽  
Principal Block ◽  
Defect Groups ◽  
Abelian Defect Groups ◽  
A Finite Group

Given an odd prime $p$ , we investigate the position of simple modules in the stable Auslander–Reiten quiver of the principal block of a finite group with noncyclic abelian Sylow $p$ -subgroups. In particular, we prove a reduction to finite simple groups. In the case that the characteristic is $3$ , we prove that simple modules in the principal block all lie at the end of their components.

scholarly journals Galois action on the principal block and cyclic Sylow subgroups

2020 ◽  
Vol 14 (7) ◽  
pp. 1953-1979
Author(s):  
Noelia Rizo ◽  
A. A. Schaeffer Fry ◽  
Carolina Vallejo
Keyword(s):  
Sylow Subgroups ◽  
Principal Block ◽  
Galois Action

scholarly journals Group structure and properties of block ideals of the group algebra

1975 ◽  
Vol 16 (1) ◽  
pp. 22-28 ◽  
Author(s):  
Wolfgang Hamernik
Keyword(s):  
Finite Group ◽  
Group Algebra ◽  
Jacobson Radical ◽  
Group Structure ◽  
Arbitrary Field ◽  
Structure And Properties ◽  
Characteristic P ◽  
Principal Block ◽  
A Finite Group

In this note relations between the structure of a finite group G and ringtheoretical properties of the group algebra FG over a field F with characteristic p > 0 are investigated. Denoting by J(R) the Jacobson radical and by Z(R) the centre of the ring R, our aim is to prove the following theorem generalizing results of Wallace [10] and Spiegel [9]:Theorem. Let G be a finite group and let F be an arbitrary field of characteristic p > 0. Denoting by BL the principal block ideal of the group algebra FG the following statements are equivalent:(i) J(B1) ≤ Z(B1)(ii) J(B1)is commutative,(iii) G is p-nilpotent with abelian Sylowp-subgroups.

scholarly journals Choice of Confounding in the 2k Factorial Design in 2b Blocks

2019 ◽  
pp. 50-56
Author(s):  
Francis C. Eze
Keyword(s):  
Factorial Design ◽  
Linear Combination ◽  
Incomplete Block ◽  
Multiplication Module ◽  
Principal Block ◽  
Randomized Design ◽  
Number Of Factors ◽  
Completely Randomized Design ◽  
Homogeneous Block ◽  
Number Of Treatment

In 2k complete factorial experiment, the experiment must be carried out in a completely randomized design. When the numbers of factors increase, the number of treatment combinations increase and it is not possible to accommodate all these treatment combinations in one homogeneous block. In this case, confounding in more than one incomplete block becomes necessary. In this paper, we considered the choice of confounding when k > 2. Our findings show that the choice of confounding depends on the number of factors, the number of blocks and their sizes. When two more interactions are to be confounded, their product module 2 should be considered and thereafter, a linear combination equation should be used in allocating the treatment effects in the principal block. Other contents in other blocks are generated by multiplication module 2 of the effects not in the principal block. Partial confounding is recommended for the interactions that cannot be confounded.

scholarly journals The Tropical Matrix Groups with Symmetric Idempotents

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Lin Yang
Keyword(s):  
Diagonal Matrix ◽  
Main Diagonal ◽  
Diagonal Block ◽  
Maximal Subgroups ◽  
Block Diagonal Matrix ◽  
Matrix Groups ◽  
Idempotent Matrix ◽  
Block Idempotent ◽  
Real Matrices ◽  
Block Diagonal

In this paper we study the semigroup Mn(T) of all n×n tropical matrices under multiplication. We give a description of the tropical matrix groups containing a diagonal block idempotent matrix in which the main diagonal blocks are real matrices and other blocks are zero matrices. We show that each nonsingular symmetric idempotent matrix is equivalent to this type of block diagonal matrix. Based upon this result, we give some decompositions of the maximal subgroups of Mn(T) which contain symmetric idempotents.

Experimental Results from Physical Model of Bidirectional Power Flow Regulator for Power Substations of Electrical Transport

2009 ◽  
Vol 25 (25) ◽  
pp. 127-132
Author(s):  
Aigars Vitols ◽  
Ivars Rankis
Keyword(s):  
Physical Model ◽  
Electrical Transport ◽  
Power Flow ◽  
Experimental Results ◽  
Principal Block ◽  
Block Scheme ◽  
Flow Regulator ◽  
Bidirectional Power Flow ◽  
Made In ◽  
Power Substations

Experimental Results from Physical Model of Bidirectional Power Flow Regulator for Power Substations of Electrical TransportThis article is about model of bidirectional power flow regulator for power substations of electrical transport. The paper presents an experimental model which is made in the laboratory of Power and electrical engineering of Riga Technical University. Also principal block scheme and principal schemes of that model are presented in the form of computer modeling as well as some main results of experiments are presented in the form of diagrams.

scholarly journals Parabolic category O, perverse sheaves on Grassmannians, Springer fibres and Khovanov homology

2009 ◽  
Vol 145 (4) ◽  
pp. 954-992 ◽  
Author(s):  
Catharina Stroppel
Keyword(s):  
Endomorphism Ring ◽  
Cohomology Ring ◽  
Injective Module ◽  
Duke Math ◽  
Khovanov Homology ◽  
Perverse Sheaves ◽  
Parabolic Subalgebra ◽  
Principal Block ◽  
Category O

AbstractFor a fixed parabolic subalgebra 𝔭 of $\mathfrak {gl}(n,\mathbb {C})$ we prove that the centre of the principal block 𝒪0𝔭 of the parabolic category 𝒪 is naturally isomorphic to the cohomology ring H*(ℬ𝔭) of the corresponding Springer fibre. We give a diagrammatic description of 𝒪0𝔭 for maximal parabolic 𝔭 and give an explicit isomorphism to Braden’s description of the category PervB(G(k,n)) of Schubert-constructible perverse sheaves on Grassmannians. As a consequence Khovanov’s algebra ℋn is realised as the endomorphism ring of some object from PervB(G(n,n)) which corresponds under localisation and the Riemann–Hilbert correspondence to a full projective–injective module in the corresponding category 𝒪0𝔭. From there one can deduce that Khovanov’s tangle invariants are obtained from the more general functorial invariants in [C. Stroppel, Categorification of the Temperley Lieb category, tangles, and cobordisms via projective functors, Duke Math. J. 126(3) (2005), 547–596] by restriction.

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