gh-36169: Implementation of representations of Lie algebras
    
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We provide an implementation of two classes of representations of Lie
algebras: the trivial representation and those defined by explicitly
giving the matrices.

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URL: #36169
Reported by: Travis Scrimshaw
Reviewer(s): Frédéric Chapoton, Travis Scrimshaw

Author: Release Manager

src/doc/en/reference/algebras/lie_algebras.rst

@@ -19,6 +19,7 @@ Lie Algebras
    sage/algebras/lie_algebras/poincare_birkhoff_witt
    sage/algebras/lie_algebras/quotient
    sage/algebras/lie_algebras/rank_two_heisenberg_virasoro
+   sage/algebras/lie_algebras/representation
    sage/algebras/lie_algebras/structure_coefficients
    sage/algebras/lie_algebras/subalgebra
    sage/algebras/lie_algebras/symplectic_derivation

src/sage/algebras/lie_algebras/lie_algebra_element.pyx

@@ -1232,9 +1232,9 @@ cdef class UntwistedAffineLieAlgebraElement(Element):
         return type(self)(self._parent, negate(self._t_dict),
                           -self._c_coeff, -self._d_coeff)
 
-    cpdef _acted_upon_(self, x, bint self_on_left) noexcept:
+    cpdef _acted_upon_(self, scalar, bint self_on_left) noexcept:
         """
-        Return ``self`` acted upon by ``x``.
+        Return ``self`` acted upon by ``scalar``.
 
         EXAMPLES::
 
@@ -1246,9 +1246,21 @@ cdef class UntwistedAffineLieAlgebraElement(Element):
             sage: -2 * x
             (-2*E[alpha[1]])#t^0 + (-2*h1)#t^-1 + -6*c + 4/5*d
         """
-        return type(self)(self._parent, scal(x, self._t_dict, self_on_left),
-                          x * self._c_coeff,
-                          x * self._d_coeff)
+        # This was copied and IDK if it still applies (TCS):
+        # With the current design, the coercion model does not have
+        # enough information to detect apriori that this method only
+        # accepts scalars; so it tries on some elements(), and we need
+        # to make sure to report an error.
+        scalar_parent = parent(scalar)
+        if scalar_parent != self._parent.base_ring():
+            # Temporary needed by coercion (see Polynomial/FractionField tests).
+            if self._parent.base_ring().has_coerce_map_from(scalar_parent):
+                scalar = self._parent.base_ring()(scalar)
+            else:
+                return None
+        return type(self)(self._parent, scal(scalar, self._t_dict, self_on_left),
+                          scalar * self._c_coeff,
+                          scalar * self._d_coeff)
 
     cpdef monomial_coefficients(self, bint copy=True) noexcept:
         """