On some graded algebras

AbstractWe show that the notions of homotopy epimorphism and homological epimorphism in the category of differential graded algebras are equivalent. As an application we obtain a characterization of acyclic maps of topological spaces in terms of induced maps of their chain algebras of based loop spaces. In the case of a universal acyclic map we obtain, for a wide class of spaces, an explicit algebraic description for these induced maps in terms of derived localization.

Download Full-text

On maximally graded algebras and Walsh functions

Reports on Mathematical Physics ◽

10.1016/0034-4877(88)90008-0 ◽

1988 ◽

Vol 26 (1) ◽

pp. 137-142 ◽

Cited By ~ 5

Author(s):

A.K. Kwaśniewski

Keyword(s):

Walsh Functions ◽

Graded Algebras

Download Full-text

The Jacobson radical of monoid-graded algebras

Tsukuba Journal of Mathematics ◽

10.21099/tkbjm/1496161828 ◽

1992 ◽

Vol 16 (1) ◽

pp. 19-52 ◽

Cited By ~ 2

Author(s):

G. Karpilovsky

Keyword(s):

Jacobson Radical ◽

Graded Algebras

Download Full-text

Some graded algebras

Analytic Pro-P Groups ◽

10.1017/cbo9780511470882.016 ◽

1999 ◽

pp. 291-310

Keyword(s):

Graded Algebras

Download Full-text

Some New Methods in the Theory of $m$-Quasi-Invariants

The Electronic Journal of Combinatorics ◽

10.37236/1877 ◽

2005 ◽

Vol 11 (2) ◽

Author(s):

J. Bell ◽

A. M. Garsia ◽

N. Wallach

Keyword(s):

Symmetric Functions ◽

Free Module ◽

Finitely Generated ◽

Graded Algebras ◽

New Approach ◽

Elementary Symmetric Functions ◽

New Methods ◽

Regular Sequences

We introduce here a new approach to the study of $m$-quasi-invariants. This approach consists in representing $m$-quasi-invariants as $N^{tuples}$ of invariants. Then conditions are sought which characterize such $N^{tuples}$. We study here the case of $S_3$ $m$-quasi-invariants. This leads to an interesting free module of triplets of polynomials in the elementary symmetric functions $e_1,e_2,e_3$ which explains certain observed properties of $S_3$ $m$-quasi-invariants. We also use basic results on finitely generated graded algebras to derive some general facts about regular sequences of $S_n$ $m$-quasi-invariants

Download Full-text

The Algebraic and Geometric Classification of Four Dimensional Superalgebras

10.26686/wgtn.16915645.v1 ◽

2021 ◽

Author(s):

◽

Aaron Armour

Keyword(s):

Classification Problem ◽

Associative Algebras ◽

New Variety ◽

Graded Algebras ◽

Finite Representation ◽

Algebraic Classification ◽

Irreducible Components ◽

Module Algebras ◽

Sweedler’S Hopf Algebra

The algebraic and geometric classification of k-algbras, of dimension fouror less, was started by Gabriel in “Finite representation type is open” [12]. Several years later Mazzola continued in this direction with his paper “Thealgebraic and geometric classification of associative algebras of dimensionfive” [21]. The problem we attempt in this thesis, is to extend the resultsof Gabriel to the setting of super (or Z2-graded) algebras — our main effortsbeing devoted to the case of superalgebras of dimension four. Wegive an algebraic classification for superalgebras of dimension four withnon-trivial Z2-grading. By combining these results with Gabriel’s we obtaina complete algebraic classification of four dimensional superalgebras. This completes the classification of four dimensional Yetter-Drinfeld modulealgebras over Sweedler’s Hopf algebra H4 given by Chen and Zhangin “Four dimensional Yetter-Drinfeld module algebras over H4” [9]. Thegeometric classification problem leads us to define a new variety, Salgn —the variety of n-dimensional superalgebras—and study some of its properties. The geometry of Salgn is influenced by the geometry of the varietyAlgn yet it is also more complicated, an important difference being thatSalgn is disconnected. While we make significant progress on the geometricclassification of four dimensional superalgebras, it is not complete. Wediscover twenty irreducible components of Salg4 — however there couldbe up to two further irreducible components.

Download Full-text