Snowflake won't allow an analytic function to be renamed

In the code below, I can do the LAG and PARTITION BY with no problem as a query. But I need it as a table. If I do CTAS, I need an alias on the column. But when I try to put an alias on it, it fails. I think this is valid SQL. But I'm using Snowflake , so I'm asking it on Super User as I fear this is a vendor issue. How can I create a table with the output of that query?

drop table a;

create table a (
    a1 varchar,
    a2 varchar
);

insert into a values ( 'a', 1 );
insert into a values ( 'a', 3 );
insert into a values ( 'a', 5 );
insert into a values ( 'a', 9 );
insert into a values ( 'b', 1 );
insert into a values ( 'b', 3 );
insert into a values ( 'b', 4 );
insert into a values ( 'c', 3 );
insert into a values ( 'c', 4 );
insert into a values ( 'c', 5 );

-- This works fine.
select a1
     , a2
     , lag(a2)
  over (partition by a1 order by a2)
  from a
;

-- This fails.
select a1
     , a2
     , lag(a2) new_col_name
  over (partition by a1 order by a2)
  from a
;

-- But if I can't name the column, I can't CTAS.
create table b as
select a1
     , a2
     , lag(a2)
  over (partition by a1 order by a2)
  from a
;

Output is:

status
A successfully dropped.
status
Table A successfully created.
number of rows inserted
                      1
number of rows inserted
                      1
number of rows inserted
                      1
number of rows inserted
                      1
number of rows inserted
                      1
number of rows inserted
                      1
number of rows inserted
                      1
number of rows inserted
                      1
number of rows inserted
                      1
number of rows inserted
                      1
A1  A2  LiteralRedacted0
b   1   NULL
b   3   1
b   4   3
c   3   NULL
c   4   3
c   5   4
a   1   NULL
a   3   1
a   5   3
a   9   5
001003 (42000): SQL compilation error:
syntax error line 4 at position 2 unexpected 'over'.
002022 (42601): SQL compilation error:
Missing column specification