Spectral isometries into commutative Banach algebras

We determine the structure of spectral isometries between unital Banach algebras under the hypothesis that the codomain is commutative.

Representation type of Jordan algebras

The problem of classification of Jordan bit-nodules over (non-semisimple) finite dimensional Jordan algebras with respect to their representation type is considered. The notions of diagram of a Jordan algebra and of Jordan tensor algebra of a bimodule are introduced and a mapping Qui is constructed which associates to the diagram of a Jordan algebra J the quiver of its universal associative enveloping algebra S(J). The main results are concerned with Jordan algebras of semi-matrix type, that is, algebras whose semi-simple component is a direct sum of Jordan matrix algebras. In this case, criterion of finiteness and tameness for one-sided representations are obtained, in terms of diagram and mapping Qui, for Jordan tensor algebras and for algebras with radical square equals to 0. (c) 2010 Elsevier Inc. All rights reserved.

Symplectic bosons, Fermi fields and super Jordan algebras

A construction relating the structures of super Lie and super Jordan algebras is proposed. This may clarify the role played by field theoretical realizations of super Jordan algebras in constructing representations of super Kač-Moody algebras. The case of OSP(m, n) and super Clifford algebras involving independent Fermi fields and symplectic bosons is discussed in detail.

Fundamental Investigations on the Isomorphism of Commutative Group Algebras in Bulgaria

The isomorphism problem of arbitrary algebraic structures plays always a central role in the study of a given algebraic object. In this paper we give the first investigations and also some basic results on the isomorphism problem of commutative group algebras in Bulgaria.

Isomorphism of Commutative Group Algebras of Finite Abelian Groups

Let a commutative ring R be a direct product of indecomposable rings with identity and let G be a finite abelian p-group. In the present paper we give a complete system of invariants of the group algebra RG of G over R when p is an invertible element in R. These investigations extend some classical results of Berman (1953 and 1958), Sehgal (1970) and Karpilovsky (1984) as well as a result of Mollov (1986).

Fundamental Investigations on the Unit Groups of Commutative Group Algebras in Bulgaria

In this paper we give the first investigations and also some basic results on the unit groups of commutative group algebras in Bulgaria. These investigations continue some classical results. Namely, it is supposed that the cardinality of the starting group is arbitrary.

A structural theorem for co-commutative Hopf algebras

Lo scopo di questa tesi è studiare alcune proprietà di base delle algebre di Hopf, strutture algebriche emerse intorno agli anni ’50 dalla topologica algebrica e dalla teoria dei gruppi algebrici, e mostrare un collegamento tra esse e le algebre di Lie. Il primo capitolo è un’introduzione basilare al concetto di prodotto tensoriale di spazi vettoriali, che verrà utilizzato nel secondo capitolo per definire le strutture di algebra, co-algebra e bi-algebra. Il terzo capitolo introduce le definizioni e alcune proprietà di base delle algebre di Hopf e di Lie, con particolare attenzione al legame tra le prime e l’algebra universale inviluppante di un’algebra di Lie. Questo legame sarà approfondito nel quarto capitolo, dedicato allo studio di una particolare classe di algebre di Hopf, quelle graduate e connesse, che terminerà con il teorema di Cartier-Quillen-Milnor-Moore, un teorema strutturale che fornisce condizioni sufficienti affinché un’algebra di Hopf sia isomorfa all’algebra universale inviluppante dei suoi elementi primitivi.

Algebraic structure for the crossing of balanced and stair nested designs

Stair nesting allows us to work with fewer observations than the most usual form of nesting, the balanced nesting. In the case of stair nesting the amount of information for the different factors is more evenly distributed. This new design leads to greater economy, because we can work with fewer observations. In this work we present the algebraic structure of the cross of balanced nested and stair nested designs, using binary operations on commutative Jordan algebras. This new cross requires fewer observations than the usual cross balanced nested designs and it is easy to carry out inference.

Joining models with stair nesting

In the stair nested designs with u factors we have u steps and a(1), ... , a(u) "active" levels. We would have a(1) observations with different levels for the first factor each of them nesting a single level of each of the remaining factors; next a(2) observations with level a(1) + 1 for the first factor and distinct levels for the second factor each nesting a fixed level of each of the remaining factors, and so on. So the number of level combinations is Sigma(u)(i=1) a(i). In meta-analysis joint treatment of different experiments is considered. Joining the corresponding models may be useful to carry out that analysis. In this work we want joining L models with stair nesting.

Study of the interactions in a three-way crossed classification model

Crossed classification models are applied in many investigations taking in consideration the existence of interaction between all factors or, in alternative, excluding all interactions, and in this case only the effects and the error term are considered. In this work we use commutative Jordan algebras in the study of the algebraic structure of these designs and we use them to obtain similar designs where only some of the interactions are considered. We finish presenting the expressions of the variance componentes estimators.

Algebraic structure for interaction on mixed models

Binary operations on commutative Jordan algebras, CJA, can be used to study interactions between sets of factors belonging to a pair of models in which one nests the other. It should be noted that from two CJA we can, through these binary operations, build CJA. So when we nest the treatments from one model in each treatment of another model, we can study the interactions between sets of factors of the first and the second models.

Orthogonal models, structure crossing, nesting and inference

We intend to study the algebraic structure of the simple orthogonal models to use them, through binary operations as building blocks in the construction of more complex orthogonal models. We start by presenting some matrix results considering Commutative Jordan Algebras of symmetric matrices, CJAs. Next, we use these results to study the algebraic structure of orthogonal models, obtained by crossing and nesting simpler ones. Then, we study the normal models with OBS, which can also be orthogonal models. We intend to study normal models with OBS (Orthogonal Block Structure), NOBS (Normal Orthogonal Block Structure), obtaining condition for having complete and suffcient statistics, having UMVUE, is unbiased estimators with minimal covariance matrices whatever the variance components. Lastly, see ([Pereira et al. (2014)]), we study the algebraic structure of orthogonal models, mixed models whose variance covariance matrices are all positive semi definite, linear combinations of known orthogonal pairwise orthogonal projection matrices, OPOPM, and whose least square estimators, LSE, of estimable vectors are best linear unbiased estimator, BLUE, whatever the variance components, so they are uniformly BLUE, UBLUE. From the results of the algebraic structure we will get explicit expressions for the LSE of these models.

Jordan Gradings on Associative Algebras

In this paper we apply the method of functional identities to the study of group gradings by an abelian group G on simple Jordan algebras, under very mild restrictions on the grading group or the base field of coefficients.

Isomorphism of Commutative Modular Group Algebras

∗ The work was supported by the National Fund “Scientific researches” and by the Ministry of Education and Science in Bulgaria under contract MM 70/91.

Special identities for Bol algebras

Bol algebras appear as the tangent algebra of Bol loops. A (left) Bol algebra is a vector space equipped with a binary operation [a, b] and a ternary operation {a, b, c} that satisfy five defining identities. If A is a left or right alternative algebra then A(b) is a Bol algebra, where [a, b] := ab - ba is the commutator and {a, b, c} := < b, c, a > is the Jordan associator. A special identity is an identity satisfied by Ab for all right alternative algebras A, but not satisfied by the free Bol algebra. We show that there are no special identities of degree <= 7, but there are special identities of degree 8. We obtain all the special identities of degree 8 in partition six-two. (C) 2011 Elsevier Inc. All rights reserved.