Expand all Collapse all | Results 1 - 4 of 4 |
1. CMB 2011 (vol 55 pp. 67)
An $E_8$ Correspondence for Multiplicative Eta-Products We describe an $E_8$ correspondence for the multiplicative
eta-products of weight at least $4$.
Keywords:We describe an E_{8} correspondence for the multiplicative eta-products of weight at leastÂ 4. Categories:11F20, 11F12, 17B60 |
2. CMB 2011 (vol 54 pp. 442)
Nondegeneracy for Lie Triple Systems and Kantor Pairs We study the transfer of nondegeneracy
between Lie triple systems and their standard Lie algebra envelopes
as well as between Kantor pairs, their associated Lie triple systems,
and their Lie algebra envelopes. We also show that simple Kantor
pairs and Lie triple systems in characteristic $0$ are
nondegenerate.
Keywords:Kantor pairs, Lie triple systems, Lie algebras Categories:17A40, 17B60, 17B99 |
3. CMB 2005 (vol 48 pp. 445)
On the Garsia Lie Idempotent The orthogonal projection of the free associative algebra onto the
free Lie algebra is afforded by an idempotent in the rational group
algebra of the symmetric group $S_n$, in each homogenous degree
$n$. We give various characterizations of this Lie idempotent and show
that it is uniquely determined by a certain unit in the group algebra
of $S_{n-1}$. The inverse of this unit, or, equivalently, the Gram
matrix of the orthogonal projection, is described explicitly. We also
show that the Garsia Lie idempotent is not constant on descent classes
(in fact, not even on coplactic classes) in $S_n$.
Categories:17B01, 05A99, 16S30, 17B60 |
4. CMB 1997 (vol 40 pp. 103)
The transfer of a commutator law from a nil-ring to its adjoint group For every field $F$ of characteristic $p\geq 0$,
we construct an example of a finite dimensional nilpotent
$F$-algebra $R$ whose adjoint group $A(R)$ is not
centre-by-metabelian, in spite of the fact that $R$ is Lie
centre-by-metabelian
and satisfies the identities $x^{2p}=0$ when $p>2$ and
$x^8=0$ when $p=2$. The
existence of such algebras answers a question raised by
A.~E.~Zalesskii, and is in contrast to
positive results obtained by Krasilnikov, Sharma and Srivastava
for Lie metabelian rings
and by Smirnov for the class Lie centre-by-metabelian nil-algebras
of exponent 4 over a field of characteristic 2 of cardinality at least 4.
Categories:16U60, 17B60 |