On the Cohomology Theory for Associative Algebras

1946 ◽  
Vol 47 (3) ◽  
pp. 568 ◽  
Author(s):  
G. Hochschild
Keyword(s):  
Cohomology Theory ◽  
Associative Algebras

scholarly journals Note on the Cohomology Groups of Associative Algebras

1953 ◽  
Vol 6 ◽  
pp. 85-92 ◽  
Author(s):  
Hirosi Nagao
Keyword(s):  
Detailed Analysis ◽  
Structural Characterization ◽  
Cohomology Theory ◽  
Cohomology Groups ◽  
Associative Algebras ◽  
3 Dimensional

The cohomology theory of associative algebras has been developed by G. liochschild [1], [2], [3], and the 1-, 2-, and 3-dimensional cohomology groups have been interpreted with reference to classical notions of structure in his papers. Recently M. Ikeda has obtained, by a detailed analysis of Hochschild’s modules, an interesting structural characterization of the class of algebras whose 2-dimensional cohomology groups are all zero [5].

scholarly journals Algebras With Vanishing n-Cohomology Groups

1954 ◽  
Vol 7 ◽  
pp. 115-131 ◽  
Author(s):  
Masatoshi Ikeda ◽  
Hiroshi Nagao ◽  
Tadashi Nakayama
Keyword(s):  
Associative Algebra ◽  
Finite Rank ◽  
Unit Element ◽  
Cohomology Theory ◽  
Cohomology Groups ◽  
Associative Algebras ◽  
Semisimple Algebras

Cohomology theory for (associative) algebras was first established in general higher dimensionalities by G. Hochschild [3], [4], [5]. Algebras with vanishing 1-cohomology groups are separable semisimple algebras ([3], Theorem 4.1). On extending and refining our recent results [6], [8], [12], we establish in the present paper the following:Let n ≧ 2. Let A be an (associative) algebra (of finite rank) possessing a unit element 1 over a field Ω, and N be its radical.

Crossed homomorphisms of Lie algebras

1966 ◽  
Vol 62 (4) ◽  
pp. 577-581 ◽  
Author(s):  
Abraham S.-T. Lue
Keyword(s):  
Lie Algebras ◽  
Equivalence Classes ◽  
Cohomology Theory ◽  
Associative Algebras ◽  
Real Numbers ◽  
Finite Dimensional ◽  
Inner Automorphisms

In an earlier paper (3), a non-abelian cohomology theory (in the dimensions 0 and 1) for associative algebras was developed. One of the objectives was to obtain equivalence classes of crossed homomorphisms by considering inner automorphisms of the coefficient-algebra. This paper is an adaptation of the methods employed there to the case of Lie algebras. Throughout, all our Lie algebras will be over the field of real numbers, and finite-dimensional.

scholarly journals Total Differentiability and Monogenicity for Functions in Algebras of Order 4

2021 ◽  
Vol 15 (2) ◽  
Author(s):  
I. Sabadini ◽  
D. C. Struppa
Keyword(s):  
Analytic Functions ◽  
Associative Algebras ◽  
Basic Tool ◽  
Algebraic Analysis ◽  
Italian School ◽  
Relevant Role

AbstractIn this paper we discuss some notions of analyticity in associative algebras with unit. We also recall some basic tool in algebraic analysis and we use them to study the properties of analytic functions in two algebras of dimension four that played a relevant role in some work of the Italian school, but that have never been fully investigated.

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