BUG: ArrowDtype raising for fixed size list (pandas-dev#55000)

* BUG: ArrowDtype raising for fixed size list

* Update v2.1.1.rst

* Update test_arrow.py

Author: phofl

doc/source/whatsnew/v2.1.1.rst

@@ -29,6 +29,7 @@ Fixed regressions
 
 Bug fixes
 ~~~~~~~~~
+- Fixed bug for :class:`ArrowDtype` raising ``NotImplementedError`` for fixed-size list (:issue:`55000`)
 - Fixed bug in :meth:`DataFrame.stack` with ``future_stack=True`` and columns a non-:class:`MultiIndex` consisting of tuples (:issue:`54948`)
 
 .. ---------------------------------------------------------------------------

pandas/core/dtypes/dtypes.py

@@ -2148,6 +2148,8 @@ def type(self):
             return CategoricalDtypeType
         elif pa.types.is_list(pa_type) or pa.types.is_large_list(pa_type):
             return list
+        elif pa.types.is_fixed_size_list(pa_type):
+            return list
         elif pa.types.is_map(pa_type):
             return list
         elif pa.types.is_struct(pa_type):

pandas/tests/extension/test_arrow.py

@@ -2992,6 +2992,15 @@ def test_groupby_count_return_arrow_dtype(data_missing):
     tm.assert_frame_equal(result, expected)
 
 
+def test_fixed_size_list():
+    # GH#55000
+    ser = pd.Series(
+        [[1, 2], [3, 4]], dtype=ArrowDtype(pa.list_(pa.int64(), list_size=2))
+    )
+    result = ser.dtype.type
+    assert result == list
+
+
 def test_arrowextensiondtype_dataframe_repr():
     # GH 54062
     df = pd.DataFrame(