Simple Virasoro modules induced from codimension one subalgebras of the positive part

We construct a new five-parameter family of simple modules over the Virasoro Lie algebra.Comment: 9 page

Whittaker categories and strongly typical Whittaker modules for Lie superalgebras

Following analogous constructions for Lie algebras, we define Whittaker modules and Whittaker categories for finite-dimensional simple Lie superalgebras. Results include a decomposition of Whittaker categories for a Lie superalgebra according to the action of an appropriate sub-superalgebra; and, for basic classical Lie superalgebras of type I, a description of the strongly typical simple Whittaker modules

Whittaker Modules for the Virasoro Algebra

Whittaker modules have been well studied in the setting of complex semisimple Lie algebras. Their definition can easily be generalized to certain other Lie algebras with triangular decomposition, including the Virasoro algebra. We define Whittaker modules for the Virasoro algebra and obtain analogues to several results from the classical setting, including a classification of simple Whittaker modules by central characters and composition series for general Whittaker modules.Comment: 14 pages; revised descriptions of references [4] and [5

Undergraduate students\u27 self-reported use of mathematics textbooks

Textbooks play an important role in undergraduate mathematics courses and have the potential to impact student learning. However, there have been few studies that describe students\u27 textbook use in detail. In this study, 1156 undergraduate students in introductory mathematics classes were surveyed, and asked to describe how they used their textbook. The results indicate that students tend to use examples, instead of the expository text, to build their mathematical understanding, which instructors may view as problematic. This way of using the textbook may be the result of the textbook structure itself, as well as students\u27 beliefs about reading and the nature of mathematics. Although many instructors may not clearly convey how they want their students to use the textbook, students do report using it more productively when they believe they are asked to do so. This suggests that instructors should carefully choose text materials to promote mathematical reasoning, and actively encourage their students to read the text in a way that supports the development of this reasoning

Associating Geometry to the Lie Superalgebra sl(1|1) and to the Color Lie Algebra sl_2^c(k)

info:eu-repo/semantics/publishe