| Title:
|
Certain partitions on a set and their applications to different classes of graded algebras (English) |
| Author:
|
Martín, Antonio J. Calderón |
| Author:
|
Dieme, Boubacar |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 (print) |
| ISSN:
|
2336-1298 (online) |
| Volume:
|
29 |
| Issue:
|
2 |
| Year:
|
2021 |
| Pages:
|
243-254 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $({\mathfrak A} , {\epsilon }_{u})$ and $({\mathfrak B} , {\epsilon }_{b})$ be two pointed sets. Given a family of three maps ${\mathcal F}=\{f_1\colon {{\mathfrak A} } \to {\mathfrak A} ; f_2\colon {{\mathfrak A} } \times {\mathfrak A} \to {\mathfrak A} ; f_3\colon {{\mathfrak A} } \times {\mathfrak A} \to {\mathfrak B} \}$, this family provides an adequate decomposition of ${\mathfrak A} \setminus \{ \epsilon _u \}$ as the orthogonal disjoint union of well-described ${\mathcal F}$-invariant subsets. This decomposition is applied to the structure theory of graded involutive algebras, graded quadratic algebras and graded weak $H^*$-algebras. (English) |
| Keyword:
|
Set |
| Keyword:
|
application |
| Keyword:
|
graded algebra |
| Keyword:
|
involutive algebra |
| Keyword:
|
quadratic algebra |
| Keyword:
|
weak $H^*$-algebra |
| Keyword:
|
structure theory |
| MSC:
|
03E75 |
| MSC:
|
08A05 |
| MSC:
|
16W50 |
| MSC:
|
17A01 |
| MSC:
|
17A45 |
| idZBL:
|
Zbl 07426421 |
| idMR:
|
MR4285754 |
| . |
| Date available:
|
2021-11-04T12:17:13Z |
| Last updated:
|
2021-12-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149192 |
| . |
| Reference:
|
[1] Ambrose, W.: Structure theorems for a special class of Banach algebras.Transactions of the American Mathematical Society, 57, 3, 1945, 364-386, JSTOR, 10.1090/S0002-9947-1945-0013235-8 |
| Reference:
|
[2] Bajo, I., Benayadi, S., Medina, A.: Symplectic structures on quadratic Lie algebras.Journal of Algebra, 316, 1, 2007, 174-188, Elsevier, 10.1016/j.jalgebra.2007.06.001 |
| Reference:
|
[3] Benayadi, S.: Structures de certaines algèbres de Lie quadratiques.Communications in Algebra, 23, 10, 1995, 3867-3887, Taylor & Francis, 10.1080/00927879508825437 |
| Reference:
|
[4] Calderón, A.J., Draper, C., Martin, C., Ndoye, D.: Orthogonal-gradings on $ H^* $-algebras.Mediterranean Journal of Mathematics, 15, 1, 2018, 1-18, Springer, 10.1007/s00009-017-1059-7 |
| Reference:
|
[5] Mira, J.A. Cuenca, Mart{í}n, A.G., Gonz{á}lez, C.M.: Structure theory for $L^{*}$-algebras.Mathematical Proceedings of the Cambridge Philosophical Society, 107, 2, 1990, 361-365, Cambridge University Press, 10.1017/S0305004100068626 |
| Reference:
|
[6] Draper, C., Martín, C.: Gradings on $\mathfrak {g}_2$.Linear Algebra and its Applications, 418, 1, 2006, 85-111, |
| Reference:
|
[7] Draper, C., Martín, C.: Gradings on the Albert algebra and on $\mathfrak {f}_4$.Revista Matemática Iberoamericana, 25, 3, 2009, 841-908, Real Sociedad Matemática Española, |
| Reference:
|
[8] Elduque, A., Kochetov, M.: Gradings on simple Lie algebras.2013, Mathematical Surveys and Monographs 189, American Mathematical Society, |
| . |
