# Group algebras

Xem 1-20 trên 59 kết quả Group algebras
• ### Đề tài " The derivation problem for group algebras "

If G is a locally compact group, then for each derivation D from L1 (G) into L1 (G) there is a bounded measure μ ∈ M (G) with D(a) = a ∗ μ − μ ∗ a for a ∈ L1 (G) (“derivation problem” of B. E. Johnson). Introduction Let A be a Banach algebra, E an A-bimodule. A linear mapping D : A → E is called a derivation, if D(a b) = a D(b) + D(a) b for all a, b ∈ A ([D, Def. 1.8.1]). For x ∈ E, we deﬁne the inner derivation adx :...

• ### Evolution Algebras and their Applications

In this book, we introduce a new type of algebra, which we call evolution algebras. These are algebras in which the multiplication tables are of a special type. They are motivated by evolution laws of genetics. We view alleles (or organelles or cells, etc,) as generators of algebras. Therefore we define the multiplication of two “alleles” Gi and Gj by Gi · Gj = 0 if i = j. However, Gi ·Gi is viewed as “self-reproduction,” so that Gi ·Gi = j pijGj, where the summation is taken over all generators Gj .

• ### Elements of abstract and linear algebra

This book is a survey of abstract algebra with emphasis on algebra tinh.Do is online for students in mathematics, computer science, and physical sciences. The rst three or four chapters can stand alone as a one semester course in abstract algebra. However, they are structured to provide the foundation for the program linear algebra. Chapter 2 is the most di cult part of the book for group written in additive notation and multiplication, and the concept of coset is confusing at rst. Chapter 2 After the book was much easier as you go along....

Algebra is used by virtually all mathematicians, be they analysts, combinatorists, com- puter scientists, geometers, logicians, number theorists, or topologists. Nowadays, ev- eryone agrees that some knowledge of linear algebra, groups, and commutative rings is necessary, and these topics are introduced in undergraduate courses. We continue their study.

• ### Lectures On The Algebraic Theory Of Fields

There are notes of course of lectures on Field theory aimed at providing the beginner with an introduction to algebraic extensions, algebraic function ﬁelds, formally real ﬁelds and valuated ﬁelds. These lectures were preceded by an elementary course on group theory, vector spaces and ideal theory of rings—especially of Noetherian rings. A knowledge of these is presupposed in these notes.

• ### Đề tài " Automorphism groups of finite dimensional simple algebras "

We show that if a ﬁeld k contains suﬃciently many elements (for instance, if k is inﬁnite), and K is an algebraically closed ﬁeld containing k, then every linear algebraic k-group over K is k-isomorphic to Aut(A ⊗k K), where A is a ﬁnite dimensional simple algebra over k. 1. Introduction In this paper, ‘algebra’ over a ﬁeld means ‘nonassociative algebra’, i.e., a vector space A over this ﬁeld with multiplication given by a linear map A ⊗ A → A, a1 ⊗ a2 → a1 a2 , subject to no a priori conditions; cf. ...

• ### Đề tài " On deformations of associative algebras "

In a classic paper, Gerstenhaber showed that ﬁrst order deformations of an associative k-algebra a are controlled by the second Hochschild cohomology group of a. More generally, any n-parameter ﬁrst order deformation of a gives, due to commutativity of the cup-product on Hochschild cohomology, a graded algebra morphism Sym• (kn ) → Ext2•bimod (a, a).

This book presents a complete account of the foundations of the theory of p-adic Lie groups. It moves on to some of the important more advanced aspects. Although most of the material is not new, it is only in recent years that p-adic Lie groups have found important applications in number theory and representation theory. These applications constitute, in fact, an increasingly active area of research. The book is designed to give to the advanced, but not necessarily graduate, student a streamlined access to the basics of the theory. It is almost self contained.

• ### On the Discrete Logarithm Problem on Algebraic Tori

Using a recent idea of Gaudry and exploiting rational repre-sentations of algebraic tori, we present an index calculus type a lgorithm for solving the discrete logarithm problem that works directly in these groups.

• ### Linear Algebra Examples c-1 Linear Equations, Matrices and Determinants

Here we collect all tables of contents of all the books on mathematics I have written so far for the publisher. In the rst list the topics are grouped according to their headlines, so the reader quickly can get an idea of where to search for a given topic.In order not to make the titles too long I have in the numbering added a for a compendium b for practical solution procedures (standard methods etc.) c for examples.

• ### Introduction to Groups

Thi s int roduc tion to Gro up The ory, wit h its emp hasis on Lie Gro ups and the ir app licat ion to the stu dy of sym metri es of the fun damen tal con stitu ents of mat ter, has its ori gin in a one -seme ster cou rse tha t I tau ght at Yal e Uni versi ty for mor e tha n ten yea rs. The cou rse was dev elope d for Sen iors, and adv anced Jun iors, maj oring in the Phy sical Sci ences .

• ### Lie Algebras

One of the important consequences of the mere existence of this formula is the following. Suppose that g is the Lie algebra of a Lie group G. Then the local structure of G near the identity, i.e. the rule for the product of two elements of G suﬃciently closed to the identity is determined by its Lie algebra g. Indeed, the exponential map is locally a diﬀeomorphism from a neighborhood of the origin in g onto a neighborhood W of the identity, and if U ⊂ W is a (possibly smaller) neighborhood of the identity such that U · U ⊂ W, the the product of a...

• ### College Algebra and Trigonometry with Application

What can your book do? End up supporting literacy worldwide! End up in the land fill. Everyone in on campus has an old book or two laying arround . Run the book drive with Better World Book to collect them and you could: Support literacy initiatives in Africa, Southeast Asia, Latin American or the U.S Raise funds for your campus group.

• ### Báo cáo toán học: "Cyclic cohomology of the group algebra of free groups "

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Journal of Operator Theory đề tài: Cyclic cohomology của đại số nhóm của các nhóm tự do...

• ### Quaternionic Structures in Mathematics and Physics

Five years after the meeting "Quaternionic Structures in Mathematics and Physics", which took place at the International School for Advanced Studies (SISSA), Trieste, 5-9 September 1994, we felt it was time to have another meeting on the same subject to bring together scientists from both areas. The second Meeting on Quaternionic Structures in Mathematics and Physics was held in Rome, 6-10 September 1999.

• ### Đề tài " Hypersurface complements, Milnor fibers and higher homotopy groups of arrangments "

The interplay between geometry and topology on complex algebraic varieties is a classical theme that goes back to Lefschetz [L] and Zariski [Z] and is always present on the scene; see for instance the work by Libgober [Li]. In this paper we study complements of hypersurfaces, with special attention to the case of hyperplane arrangements as discussed in Orlik-Terao’s book [OT1]. Theorem 1 expresses the degree of the gradient map associated to any homogeneous polynomial h as the number of n-cells that have to be added to a generic hyperplane section D(h) ∩ H to obtain the complement in...

• ### Đề tài " Unique decomposition of tensor products of irreducible representations of simple algebraic groups "

We show that a tensor product of irreducible, ﬁnite dimensional representations of a simple Lie algebra over a ﬁeld of characteristic zero determines the individual constituents uniquely. This is analogous to the uniqueness of prime factorisation of natural numbers. 1. Introduction 1.1. Let g be a simple Lie algebra over C. The main aim of this paper is to prove the following unique factorisation of tensor products of irreducible, ﬁnite dimensional representations of g:

• ### Đề tài " On finitely generated profinite groups, I: strong completeness and uniform bounds "

We prove that in every ﬁnitely generated proﬁnite group, every subgroup of ﬁnite index is open; this implies that the topology on such groups is determined by the algebraic structure. This is deduced from the main result about ﬁnite groups: let w be a ‘locally ﬁnite’ group word and d ∈ N. Then there exists f = f (w, d) such that in every d-generator ﬁnite group G, every element of the verbal subgroup w(G) is equal to a product of f w-values.

• ### Đề tài " Geometric Langlands duality and representations of algebraic groups over commutative rings "

In this paper we give a geometric version of the Satake isomorphism [Sat]. As such, it can be viewed as a ﬁrst step in the geometric Langlands program. The connected complex reductive groups have a combinatorial classiﬁcation by their root data. In the root datum the roots and the co-roots appear in a symmetric manner and so the connected reductive algebraic groups come ˇ in pairs.