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vbraun merged 2 commits into from
Jul 24, 2024
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Update ncsf.py documentation #38372

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Update ncsf.py
0-andy-0 Jul 15, 2024
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Update ncsf.py
0-andy-0 Jul 15, 2024
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7 changes: 5 additions & 2 deletions src/sage/combinat/ncsf_qsym/ncsf.py
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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
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