fix the infinite loop in lie algebra

src/sage/algebras/lie_algebras/lie_algebra.py

@@ -1240,9 +1240,34 @@ def _element_constructor_(self, x):
             -[1, 3, 2] + [3, 2, 1]
             sage: L(2)
             2*[1, 2, 3]
+
+        Test that constructing elements from vectors works correctly
+        (this used to cause infinite recursion)::
+
+            sage: gl = lie_algebras.gl(QQ, 2)
+            sage: v = gl.an_element().to_vector()
+            sage: gl(v) == gl.an_element()
+            True
+
+        Test that morphisms can be constructed (this used to fail with
+        RecursionError)::
+
+            sage: gl = lie_algebras.gl(QQ, 2)
+            sage: phi = gl.morphism({e: e for e in gl.gens()})
+            sage: all(phi(e) == e for e in gl.gens())
+            True
         """
         if isinstance(x, list) and len(x) == 2:
             return self(x[0])._bracket_(self(x[1]))
+
+        # Check if x is a vector from the module to avoid infinite recursion
+        # when constructing elements from vectors (e.g., in morphism construction)
+        try:
+            if hasattr(x, 'parent') and x.parent() == self.module():
+                return self.from_vector(x)
+        except (AttributeError, NotImplementedError):
+            pass
+
         return self.element_class(self, self._assoc(x))
 
     def associative_algebra(self):