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[unknown2]

100%
Krówczyński M. M.
Didactica Mathematicae
|
2018
|
tom 40
2
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Weak invertibility and strong spectrum

100%
Meyer M. J.
Studia Mathematica
|
1993
|
tom 105
|
nr 3
255-269
EN
A notion of weak invertibility in a unital associative algebra A and a corresponding notion of strong spectrum of an element of A is defined. It is shown that many relationships between the Jacobson radical, the group of invertibles and the spectrum have analogues relating the strong radical, the set of weakly invertible elements and the strong spectrum. The nonunital case is also discussed. A characterization is given of all (submultiplicative) norms on A in which every modular maximal ideal M ⊆ A is closed.
3
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Left-symmetric algebras, or pre-Lie algebras in geometry and physics

51%
Burde D.
Open Mathematics
|
2006
|
tom 4
|
nr 3
323-357
EN
In this survey article we discuss the origin, theory and applications of left-symmetric algebras (LSAs in short) in geometry in physics. Recently Connes, Kreimer and Kontsevich have introduced LSAs in mathematical physics (QFT and renormalization theory), where the name pre-Lie algebras is used quite often. Already Cayley wrote about such algebras more than hundred years ago. Indeed, LSAs arise in many different areas of mathematics and physics. We attempt to give a survey of the fields where LSAs play an important role. Furthermore we study the algebraic theory of LSAs such as structure theory, radical theory, cohomology theory and the classification of simple LSAs. We also discuss applications to faithful Lie algebra representations.
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