Skip to content

Commit

Permalink
Update ncsf.py
Browse files Browse the repository at this point in the history
Correction lines 184-189: Psi is not the tensor algebra on the primitives but on the generators of this free Lie algebra.
  • Loading branch information
0-andy-0 authored Jul 15, 2024
1 parent 2e5cb46 commit 6906489
Showing 1 changed file with 5 additions and 2 deletions.
7 changes: 5 additions & 2 deletions src/sage/combinat/ncsf_qsym/ncsf.py
Original file line number Diff line number Diff line change
Expand Up @@ -182,8 +182,11 @@ class NonCommutativeSymmetricFunctions(UniqueRepresentation, Parent):
bialgebra structure, which cooperates with the grading to form a
connected graded bialgebra. Thus, as any connected graded bialgebra,
``Psi`` is a Hopf algebra. Over ``QQ`` (or any other `\QQ`-algebra),
this Hopf algebra ``Psi`` is isomorphic to the tensor algebra of
its space of primitive elements.
this Hopf algebra ``Psi`` is isomorphic to the universal enveloping
algebra of its space of primitive elements. Here, the primitives
form a countably generated free Lie algebra, so ``Psi`` is isomorphic
to the tensor algebra on a countably infinite dimensional vector
space.
The antipode is an anti-algebra morphism; in the ``Psi`` basis, it
sends the generators to their opposites and changes their sign if
Expand Down

0 comments on commit 6906489

Please sign in to comment.