Constructing Heisenberg Group from its Lie Algebra

Описание к видео Constructing Heisenberg Group from its Lie Algebra

The non-commutative group multiplication of R^3 that turns it into the Heisenberg group is not something one would guess out of blue. So, how does one naturally recover this operation?

There are two answers: 1) identifying R^3 with the upper-triangular matrices with the usual matrix product, 2) in a deeper level, from its Lie algebra. The Heisenberg group's Lie algebra with just one nontrivial bracket is the simplest non-trivial 3 dimensional (real) lie algebra. We then use the amazing Baker-Campbell-Hausdorff formula to construct the group operation from the brackets.

Комментарии

Информация по комментариям в разработке

Похожие видео