| Autor: |
Michiel Hazewinkel |
| Jazyk: |
angličtina |
| Rok vydání: |
2012 |
| Předmět: |
|
| Zdroj: |
Axioms, Vol 1, Iss 2, Pp 149-154 (2012) |
| Druh dokumentu: |
article |
| ISSN: |
2075-1680 |
| DOI: |
10.3390/axioms1020149 |
| Popis: |
Let NSymm be the Hopf algebra of non-commutative symmetric functions (in an infinity of indeterminates): . It is shown that an associative algebra A with a Hasse-Schmidt derivation ) on it is exactly the same as an NSymm module algebra. The primitives of NSymm act as ordinary derivations. There are many formulas for the generators in terms of the primitives (and vice-versa). This leads to formulas for the higher derivations in a Hasse-Schmidt derivation in terms of ordinary derivations, such as the known formulas of Heerema and Mirzavaziri (and also formulas for ordinary derivations in terms of the elements of a Hasse-Schmidt derivation). These formulas are over the rationals; no such formulas are possible over the integers. Many more formulas are derivable. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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