On the Property M Conjecture for the Heisenberg Lie Algebra
نویسندگان
چکیده
We prove a fundamental case of a conjecture of the first author which expresses the homology of the extension of the Heisenberg Lie algebra by C[t]/(t) in terms of the homology of the Heisenberg Lie algebra itself. More specifically, we show that both the 0 and k + 1 x-graded components of homology of this extension of the 3-dimensional Heisenberg Lie algebra have dimension 3 by constructing a simple basis for cohomology.
منابع مشابه
Hilbert Schemes of Points on Surfaces and Heisenberg Algebras
In this article, we throw a bridge between two objects which are unrelated at rst sight. One is the in nite dimensional Heisenberg algebra (simply the Heisenberg algebra, later) which plays a fundamental role in the representation theory of the a ne Lie algebras. The other is the Hilbert schemes of points on a complex surface appearing in the algebraic geometry. As we will explain soon, the Hei...
متن کامل$L^p$-Conjecture on Hypergroups
In this paper, we study $L^p$-conjecture on locally compact hypergroups and by some technical proofs we give some sufficient and necessary conditions for a weighted Lebesgue space $L^p(K,w)$ to be a convolution Banach algebra, where $1<p<infty$, $K$ is a locally compact hypergroup and $w$ is a weight function on $K$. Among the other things, we also show that if $K$ is a locally compact hyper...
متن کاملCharacterization of Simple Highest Weight Modules
We prove that for simple complex finite dimensional Lie algebras, affine Kac-Moody Lie algebras, the Virasoro algebra and the Heisenberg-Virasoro 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.
متن کاملMonomial Irreducible sln-Modules
In this article, we introduce monomial irreducible representations of the special linear Lie algebra $sln$. We will show that this kind of representations have bases for which the action of the Chevalley generators of the Lie algebra on the basis elements can be given by a simple formula.
متن کاملThe Lie Algebra of Smooth Sections of a T-bundle
In this article, we generalize the concept of the Lie algebra of vector fields to the set of smooth sections of a T-bundle which is by definition a canonical generalization of the concept of a tangent bundle. We define a Lie bracket multiplication on this set so that it becomes a Lie algebra. In the particular case of tangent bundles this Lie algebra coincides with the Lie algebra of vector fie...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 99 شماره
صفحات -
تاریخ انتشار 2002