All Questions
1 question
13
votes
1
answer
497
views
What's the dimension of the Lie algebra generated by transpositions on $n$ objects?
Define a Lie bracket on the group algebra of the permutation group $S_n$ in the following way:
$$[\sigma, \tau] = \sigma\circ\tau - \tau\circ\sigma,$$
where $\sigma, \tau \in S_n$, and the ...