scholarly journals Matrix units and generic degrees for the Ariki–Koike algebras

2004 ◽  
Vol 281 (2) ◽  
pp. 695-730 ◽  
Author(s):  
Andrew Mathas
Keyword(s):  
Matrix Units

Ultrastructure of Gene Transcription in Spermatocytes of Trichosia pubescens Morgante, 1969 (Diptera: Sciaridae)

1976 ◽  
Vol 31 (3-4) ◽  
pp. 186-189 ◽  
Author(s):  
J.M. Amabis ◽  
K. K. Nair
Keyword(s):  
Gene Transcription ◽  
Gradual Increase ◽  
Christmas Tree ◽  
Ribosomal Cistrons ◽  
Matrix Units

Abstract In spread preparations of whole spermatocytes of Trichosia pubescens the ribosomal transcription units could be identified by virtue of their “Christmas-tree-like” morphology. The ultrastructural features of these matrices are similar to those described in other eucaryotes. However, in contrast to the previously described systems the “spacer” unit between these matrix units is very small or non-existent at all. In addition, axial fibers displaying much longer lateral fibrils, irregularly spaced, and not as closely packed as in the ribosomal cistrons, were found. These are likely to represent active nonribosomal transcription. In a few instances these lateral fibrils show a gradual increase in their length.

MATRIX UNITS FOR THE GROUP ALGEBRA kGf = k((ℤ2 × ℤ2) ≀ Sf)

2009 ◽  
Vol 02 (02) ◽  
pp. 255-277
Author(s):  
B. Sivakumar
Keyword(s):  
Group Algebra ◽  
Irreducible Representations ◽  
Complete Set ◽  
Matrix Units

The irreducible representations of the group Gf := (ℤ2 × ℤ2) ≀ Sf are indexed by 4-partitions of f, i.e., by the set {[α]3[β]2[γ]1[δ]0|α ⊢ u3, β ⊢ u2, γ ⊢ u1, δ ⊢ u0, u0 + u1 + u2 + u3 = f}. This set is in 1 - 1 correspondence with partitions of 4f whose 4-core is empty. In this paper we construct the inequivalent irreducible representations of Gf. We also compute a complete set of seminormal matrix units for the group algebra kGf.

scholarly journals A characterization of the semigroup of matrix units

1980 ◽  
Vol 29 (3) ◽  
pp. 291-296
Author(s):  
Bernard R. Gelbaum ◽  
Stephen Schanuel
Keyword(s):  
Subject Classification ◽  
M 10 ◽  
20 M 10 ◽  
The Matrix ◽  
Matrix Units

AbstractLet I be a set and let (I) denote the set consisting of the 0 matrix over I × I and the matrix units over I × I. Then for x, z in (I) and x≠0≠z, xyz≠0 has precisely one solution y. This and several other statements are shown to be equivalent characterizations of (I) regarded as a semigroup with zero.1980 Mathematics subject classification (Amer. Math. Soc.): 20 M 10.

scholarly journals On Topological Semigroups of Matrix Units

2005 ◽  
Vol 71 (3) ◽  
pp. 389-400 ◽  
Author(s):  
Oleg V. Gutik ◽  
Kateryna P. Pavlyk
Keyword(s):  
Topological Semigroups ◽  
Matrix Units

scholarly journals On the generators of elementary subgroups of general linear groups

1996 ◽  
Vol 38 (1) ◽  
pp. 1-10 ◽  
Author(s):  
A. W. Mason
Keyword(s):  
Commutative Rings ◽  
General Linear ◽  
Linear Groups ◽  
General Linear Groups ◽  
Simple Set ◽  
Matrix Units

Let R be a ring with identity and let Eij ∈ Mn(R) be the usual n X n matrix units, where n ≥ 2 and 1≤i, j≤N. Let En(R) be the subgroup of GLn(R) generated by all Tij(q where r ∈ R and i ≄ j. For each (two-sided) R-ideal q let En(R, q) be the normal subgroup of En(R) generated by Tij(q), where q ∈ q. The subgroup En(R, q) plays an important role in the theory of GLn(R). For example, Vaserˇstein has proved that, for a larger class of rings (which includes all commutative rings), every subgroup S of GLn(R), when R ∈ and n≥3, contains the subgroup En(R, q0), where q0 is the R-ideal generated by αij, rαij-αjjr (i ≄ j, r ∈ R), for all (αij) ∈ S. (See [13, Theorem 1].) In addition Vaseršstein has shown that, for the same class of rings, En(R, q) has a simple set of generators when n ≥ 3. Let Ên(R, q) be the subgroup of En(R, q) generated by Tij(r)Tij(q)Tij(−r), where r ∈ R, q ∈ q. Then Ên(R, q) = En(R, q), for all q, when R ∈ and n ≥ 3.(See [13, Lemma 8].)

scholarly journals Matrix units associated with the split basis of a Leonard pair

2006 ◽  
Vol 418 (2-3) ◽  
pp. 775-787 ◽  
Author(s):  
Kazumasa Nomura ◽  
Paul Terwilliger
Keyword(s):  
Leonard Pair ◽  
Matrix Units

scholarly journals Regulation of transcription of genes of ribosomal rna during amphibian oogenesis. A biochemical and morphological study.

1976 ◽  
Vol 69 (2) ◽  
pp. 465-489 ◽  
Author(s):  
U Scheer ◽  
M F Trendelenburg ◽  
W W Franke
Keyword(s):  
Transcriptional Control ◽  
Morphological Changes ◽  
Rrna Genes ◽  
Synthetic Activity ◽  
Rrna Synthesis ◽  
Regulation Of Transcription ◽  
Uridine Uptake ◽  
Triturus Alpestris ◽  
Matrix Units

Natural changes in the transcription of rRNA genes were studied in nucleoli from three oogenic stages of the newt Triturus alpestris with electron microscope, auto-radiographic, and biochemical techniques. From determinations of the uridine triphosphate pool sizes and [3H]uridine uptake, phosphorylation, and incorporation into 28S and 18S rRNAs in vivo it was estimated that the rate of rRNA synthesis was about 0.01% in previtellogenic oocytes and 13% in mature oocytes when compared to midvitellogenesis. Spread preparations of nucleoli showed significant morphological changes in the transcriptional complexes. The total number of lateral fibrils, i.e., ribonucleoproteins containing the nascent rRNA precursor, were drastically decreased in stages of reduced synthetic activity. This indicates that rRNA synthesis is regulated primarily at the level of transcription. The resulting patterns of fibril coverage of the nucleolar chromatin axes revealed a marked heterogeneity. On the same nucleolar axis occurred matrix units that were completely devoid of lateral fibrils, matrix units that were almost fully covered with lateral fibrils, and various forms of matrix units with a range of lateral fibril densities intermediate between the two extremes. Granular particles that were tentatively identified as RNA polymerase molecules were not restricted to the transciptional complexes. They were observed, although less regularly and separated by greater distances, in untranscribed spacer regions as well as in untranscribed gene intercepts. The results show that the pattern of transcriptional control of rRNA genes differs widely in different genes, even in the same genetic unit.

Twisted matrix units semigroup algebras

1967 ◽  
Vol 34 (3) ◽  
pp. 417-423 ◽  
Author(s):  
W. Edwin Clark
Keyword(s):  
Semigroup Algebras ◽  
Matrix Units
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