1. CMB 2014 (vol 58 pp. 69)
 Fulp, Ronald Owen

Correction to "Infinite Dimensional DeWitt Supergroups and Their Bodies"
The Theorem below is a correction to Theorem
3.5 in the article
entitled " Infinite Dimensional DeWitt Supergroups and Their
Bodies" published
in Canad. Math. Bull. Vol. 57 (2) 2014 pp. 283288. Only part
(iii) of that Theorem
requires correction. The proof of Theorem 3.5 in the original
article failed to separate
the proof of (ii) from the proof of (iii). The proof of (ii)
is complete once it is established
that $ad_a$ is quasinilpotent for each $a$ since it immediately
follows that $K$
is quasinilpotent. The proof of (iii) is not complete
in the original article. The revision appears as the proof of
(iii) of the revised Theorem below.
Keywords:super groups, body of super groups, Banach Lie groups Categories:58B25, 17B65, 81R10, 57P99 

2. CMB 2012 (vol 56 pp. 606)
 Mazorchuk, Volodymyr; Zhao, Kaiming

Characterization of Simple Highest Weight Modules
We prove that for simple complex finite dimensional
Lie algebras, affine KacMoody Lie algebras, the
Virasoro algebra and the HeisenbergVirasoro algebra,
simple highest weight modules are characterized
by the property that all positive root elements
act on these modules locally nilpotently. We
also show that this is not the case for higher rank
Virasoro and for Heisenberg algebras.
Keywords:Lie algebra, highest weight module, triangular decomposition, locally nilpotent action Categories:17B20, 17B65, 17B66, 17B68 

3. CMB 2011 (vol 54 pp. 519)
4. CMB 2008 (vol 51 pp. 298)
 Tocón, Maribel

The Kostrikin Radical and the Invariance of the Core of Reduced Extended Affine Lie Algebras
In this paper we prove that the Kostrikin radical of an extended affine Lie algebra of
reduced type coincides with the center of its core, and use this characterization to get a typefree
description of the core of such algebras. As a consequence we get that the core of an extended affine
Lie algebra of reduced type is invariant under the automorphisms of the algebra.
Keywords:extended affine Lie algebra, Lie torus, core, Kostrikin radical Categories:17B05, 17B65 

5. CMB 2003 (vol 46 pp. 597)
 Neeb, KarlHermann; Penkov, Ivan

Cartan Subalgebras of $\mathfrak{gl}_\infty$
Let $V$ be a vector space over a field $\mathbb{K}$ of characteristic
zero and $V_*$ be a space of linear functionals on $V$ which separate
the points of $V$. We consider $V\otimes V_*$ as a Lie algebra of
finite rank operators on $V$, and set $\mathfrak{gl} (V,V_*) :=
V\otimes V_*$. We define a Cartan subalgebra of $\mathfrak{gl}
(V,V_*)$ as the centralizer of a maximal subalgebra every element of
which is semisimple, and then give the following description of all
Cartan subalgebras of $\mathfrak{gl} (V,V_*)$ under the assumption
that $\mathbb{K}$ is algebraically closed. A subalgebra of
$\mathfrak{gl} (V,V_*)$ is a Cartan subalgebra if and only if it
equals $\bigoplus_j \bigl( V_j \otimes (V_j)_* \bigr) \oplus (V^0 \otimes
V_*^0)$ for some onedimensional subspaces $V_j \subseteq V$ and
$(V_j)_* \subseteq V_*$ with $(V_i)_* (V_j) = \delta_{ij} \mathbb{K}$
and such that the spaces $V_*^0 = \bigcap_j (V_j)^\bot \subseteq V_*$
and $V^0 = \bigcap_j \bigl( (V_j)_* \bigr)^\bot \subseteq V$ satisfy
$V_*^0 (V^0) = \{0\}$. We then discuss explicit constructions of
subspaces $V_j$ and $(V_j)_*$ as above. Our second main result claims
that a Cartan subalgebra of $\mathfrak{gl} (V,V_*)$ can be described
alternatively as a locally nilpotent selfnormalizing subalgebra whose
adjoint representation is locally finite, or as a subalgebra
$\mathfrak{h}$ which coincides with the maximal locally nilpotent
$\mathfrak{h}$submodule of $\mathfrak{gl} (V,V_*)$, and such that the
adjoint representation of $\mathfrak{h}$ is locally finite.
Categories:17B65, 17B20 

6. CMB 2003 (vol 46 pp. 529)
7. CMB 2002 (vol 45 pp. 567)
 De Sole, Alberto; Kac, Victor G.

Subalgebras of $\gc_N$ and Jacobi Polynomials
We classify the subalgebras of the general Lie conformal algebra
$\gc_N$ that act irreducibly on $\mathbb{C} [\partial]^N$ and that
are normalized by the sl$_2$part of a Virasoro element. The
problem turns out to be closely related to classical Jacobi
polynomials $P_n^{(\sigma,\sigma)}$, $\sigma \in \mathbb{C}$. The
connection goes both wayswe use in our classification some
classical properties of Jacobi polynomials, and we derive from the
theory of conformal algebras some apparently new properties of
Jacobi polynomials.
Categories:17B65, 17B68, 17B69, 33C45 

8. CMB 2002 (vol 45 pp. 672)
 Rao, S. Eswara; Batra, Punita

A New Class of Representations of EALA Coordinated by Quantum Tori in Two Variables
We study the representations of extended affine Lie algebras
$s\ell_{\ell+1} (\mathbb{C}_q)$ where $q$ is $N$th primitive root of
unity ($\mathbb{C}_q$ is the quantum torus in two variables). We
first prove that $\bigoplus s\ell_{\ell+1} (\mathbb{C})$ for a
suitable number of copies is a quotient of $s\ell_{\ell+1}
(\mathbb{C}_q)$. Thus any finite dimensional irreducible module for
$\bigoplus s\ell_{\ell+1} (\mathbb{C})$ lifts to a representation of
$s\ell_{\ell+1} (\mathbb{C}_q)$. Conversely, we prove that any finite
dimensional irreducible module for $s\ell_{\ell+1} (\mathbb{C}_q)$
comes from above. We then construct modules for the extended affine
Lie algebras $s\ell_{\ell+1} (\mathbb{C}_q) \oplus \mathbb{C} d_1
\oplus \mathbb{C} d_2$ which is integrable and has finite dimensional
weight spaces.
Categories:17B65, 17B66, 17B68 

9. CMB 2002 (vol 45 pp. 623)