scholarly journals Extension of the Newton–Puiseux algorithm to the case of a nonzero characteristic ground field. I

2017 ◽  
Vol 28 (6) ◽  
pp. 825-853 ◽  
Author(s):  
A. L. Chistov
Keyword(s):  
Ground Field ◽  
Nonzero Characteristic

scholarly journals CHARACTER CLUSTERS FOR LIE ALGEBRA MODULES OVER A FIELD OF NONZERO CHARACTERISTIC

2013 ◽  
Vol 89 (2) ◽  
pp. 234-242 ◽  
Author(s):  
DONALD W. BARNES
Keyword(s):  
Lie Algebra ◽  
Saturated Formation ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Direct Sum ◽  
Finite Dimensional ◽  
Nonzero Characteristic ◽  
Composition Factors

AbstractFor a Lie algebra $L$ over an algebraically closed field $F$ of nonzero characteristic, every finite dimensional $L$-module can be decomposed into a direct sum of submodules such that all composition factors of a summand have the same character. Using the concept of a character cluster, this result is generalised to fields which are not algebraically closed. Also, it is shown that if the soluble Lie algebra $L$ is in the saturated formation $\mathfrak{F}$ and if $V, W$ are irreducible $L$-modules with the same cluster and the $p$-operation vanishes on the centre of the $p$-envelope used, then $V, W$ are either both $\mathfrak{F}$-central or both $\mathfrak{F}$-eccentric. Clusters are used to generalise the construction of induced modules.

scholarly journals Modular Jordan nilalgebras

1994 ◽  
Vol 37 (1) ◽  
pp. 1-12
Author(s):  
Jose Angel Anquela
Keyword(s):  
Ground Field

In this paper we give a classification up to isomorphism of Jordan nilalgebras whose lattices of subalgebras are modular when the ground field is algebraically closed.

scholarly journals Free non-associative principal train algebras

1984 ◽  
Vol 27 (3) ◽  
pp. 313-319 ◽  
Author(s):  
P. Holgate
Keyword(s):  
Finite Number ◽  
Ground Field ◽  
Linear Forms ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
The Senses ◽  
Special Train ◽  
Complex Coefficients ◽  
Infinite Linear

The definitions of finite dimensional baric, train, and special train algebras, and of genetic algebras in the senses of Schafer and Gonshor (which coincide when the ground field is algebraically closed, and which I call special triangular) are given in Worz-Busekros's monograph [8]. In [6] I introduced applications requiring infinite dimensional generalisations. The elements of these algebras were infinite linear forms in basis elements a0, a1,… and complex coefficients such that In this paper I consider only algebras whose elements are forms which only a finite number of the xi are non zero.

HEURISTICS FOR -CLASS TOWERS OF REAL QUADRATIC FIELDS

2019 ◽  
pp. 1-24
Author(s):  
Nigel Boston ◽  
Michael R. Bush ◽  
Farshid Hajir
Keyword(s):  
Infinite Order ◽  
Quadratic Field ◽  
Imaginary Quadratic Field ◽  
Ideal Class ◽  
Real Quadratic Field ◽  
Ground Field ◽  
Real Quadratic Fields ◽  
Ideal Class Groups ◽  
Formula Group ◽  
Real Quadratic

Let $p$ be an odd prime. For a number field $K$ , we let $K_{\infty }$ be the maximal unramified pro- $p$ extension of  $K$ ; we call the group $\text{Gal}(K_{\infty }/K)$ the $p$ -class tower group of  $K$ . In a previous work, as a non-abelian generalization of the work of Cohen and Lenstra on ideal class groups, we studied how likely it is that a given finite $p$ -group occurs as the $p$ -class tower group of an imaginary quadratic field. Here we do the same for an arbitrary real quadratic field $K$ as base. As before, the action of $\text{Gal}(K/\mathbb{Q})$ on the $p$ -class tower group of $K$ plays a crucial role; however, the presence of units of infinite order in the ground field significantly complicates the possibilities for the groups that can occur. We also sharpen our results in the imaginary quadratic field case by removing a certain hypothesis, using ideas of Boston and Wood. In the appendix, we show how the probabilities introduced for finite $p$ -groups can be extended in a consistent way to the infinite pro- $p$ groups which can arise in both the real and imaginary quadratic settings.

scholarly journals Wonderful compactifications of Bruhat-Tits buildings

2017 ◽  
Vol Volume 1 ◽  
Author(s):  
Bertrand Remy ◽  
Amaury Thuillier ◽  
Annette Werner
Keyword(s):  
Local Field ◽  
Semisimple Group ◽  
The Other ◽  
Analytic Space ◽  
Ground Field ◽  
Berkovich Analytic Space ◽  
Euclidean Building ◽  
The Relationship

Given a split semisimple group over a local field, we consider the maximal Satake-Berkovich compactification of the corresponding Euclidean building. We prove that it can be equivariantly identified with the compactification which we get by embedding the building in the Berkovich analytic space associated to the wonderful compactification of the group. The construction of this embedding map is achieved over a general non-archimedean complete ground field. The relationship between the structures at infinity, one coming from strata of the wonderful compactification and the other from Bruhat-Tits buildings, is also investigated.

scholarly journals Tangible Cultural Heritage Re-Appropriation Towards A New Urban Centrality. A Critical Crossroad In Semi-Peripheral Eastern Riverside Lisbon

2020 ◽  
Vol 13 (3) ◽  
pp. 139-146
Author(s):  
Joao C. Martins
Keyword(s):  
Cultural Heritage ◽  
Urban Areas ◽  
Urban Regeneration ◽  
Ground Level ◽  
Ground Field ◽  
Public And Private ◽  
Positive Effects ◽  
The Creation ◽  
Tangible Culture ◽  
Private Investors

. The transformation of decayed semi-peripheral riverside areas and its Tangible Culture Heritage is presented today as a contributing factor in urban regeneration by several public preservation bodies and agendas, as well as privately led investment. These practices demand the economic and symbolic valorization of abandoned Tangible Cultural Heritage, where the social coexistence of residents, workers and visitors is seen as a smoother urban integration of these deprived territories and their communities into the surrounding contemporary cities.We’ll focus our approach on socio-spatial changes occurring in Marvila and Beato, presented today as new urban areas in which to financially invest after the 2011 economic crisis occurred in Portugal, discussing public and private re- appropriation of Old Palaces, Convents and Farms and Reconverted Warehouses (industrial and commercial); towards the creation of a new urban centrality in Lisbon. In this case, public ground-field intervention established a culture led regeneration process, with the creation of a municipal library, a crucial point in the cultural use of this space, community participation and gathering. Dealing with private investors, despite the positive effects, such as a reduction in unemployment, economic diversification and re-use of urban voids, there is always the possibility of undesired consequences. This paper argues, and the research experiments in many European cities show us that the ambition to improve the image of these deprived areas, despite somGonzalex encouraging ground level achievements, has unwanted or unexpected outcomes, starting as urban regeneration practices, often sliding towards gentrification, where local public powers have a determinant role.

High Order Derivations and High Order Lie-Like Elements

1972 ◽  
Vol 24 (6) ◽  
pp. 1154-1163
Author(s):  
S. T. Chang
Keyword(s):  
High Order ◽  
Ground Field ◽  
Divided Powers

We can define high order derivations of an algebra into the ground field by diagrams. Then consider the same diagrams in t he category of coalgebras. By reversing all t he arrows in these diagrams, we come to a new notion - high order Lie-like elements of a coalgebra. These elements are useful in the study of the structure of coalgebras and sequences of divided powers.

On the Cohomology of Moduli of Vector Bundles and the Tamagawa Number of SLn

2006 ◽  
Vol 58 (5) ◽  
pp. 1000-1025 ◽  
Author(s):  
Ajneet Dhillon
Keyword(s):  
Vector Bundles ◽  
Hodge Structure ◽  
Betti Numbers ◽  
Mixed Hodge Structure ◽  
Projective Curve ◽  
Ground Field ◽  
Smooth Projective Curve ◽  
Poincaré Polynomial ◽  
Moduli Stack ◽  
Moduli Of Vector Bundles

AbstractWe compute some Hodge and Betti numbers of the moduli space of stable rank r, degree d vector bundles on a smooth projective curve. We do not assume r and d are coprime. In the process we equip the cohomology of an arbitrary algebraic stack with a functorial mixed Hodge structure. This Hodge structure is computed in the case of the moduli stack of rank r, degree d vector bundles on a curve. Our methods also yield a formula for the Poincaré polynomial of the moduli stack that is valid over any ground field. In the last section we use the previous sections to give a proof that the Tamagawa number of SLn is one.

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