In this paper we construct physical systems with ℤ2×ℤ2-graded symmetries. There are two different structures:ℤ2×ℤ2-graded Lie algebras andℤ2×ℤ2-graded Lie superalgebras. Physical models with the ...latter symmetries can be seen as generalizations of supersymmetric models. The systems described by ℤ2 × ℤ2-graded Lie algebras have not been investigated yet (up to our knowledge). We present examples of physical models invariant under each one of both kinds of graded structures.
Let be the complex simple Lie algebra of type B2. In this paper, we give the explicit generators of the center of the quantum group We also study the twisted Whittaker modules over and all ...nonsingular twisted Whittaker modules are classified.
Abstract
Let
A
be an associative algebra over a field of any characteristic with involution and let
K
=
skew
(
A
) = { a ∈
A
|
a
* = −
a
} be its corresponding sub-algebra under the Lie product
a, b
... =
ab
−
ba
for all
a, b
∈
A
. In this paper, inner ideals of such Lie algebras were defined, considered, studied, and classified. Some examples and results were provided. It is proved that for every Jordan-Lie inner ideal of
K
, one can find an idempotent
e
∈
A
such that this inner ideal may be written in the form
eK e
*. It is also proved inner ideals of such Lie algebras are regular.
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