GENERATED * AS IDENTITY should not create a primary key

h2/src/main/org/h2/command/Parser.java

@@ -4887,7 +4887,6 @@ public class Parser {
                 }
                 read(CLOSE_PAREN);
             }
-            column.setPrimaryKey(true);
             column.setAutoIncrement(true, start, increment);
         }
         if (readIf(ON)) {

h2/src/test/org/h2/test/scripts/ddl/createTable.sql

@@ -95,3 +95,22 @@ SELECT COLUMN_NAME, IS_VISIBLE FROM INFORMATION_SCHEMA.COLUMNS WHERE TABLE_NAME
 
 DROP TABLE TEST;
 > ok
+
+CREATE TABLE TEST1(ID IDENTITY);
+> ok
+
+CREATE TABLE TEST2(ID BIGINT IDENTITY);
+> ok
+
+CREATE TABLE TEST3(ID BIGINT GENERATED BY DEFAULT AS IDENTITY);
+> ok
+
+SELECT CONSTRAINT_TYPE, TABLE_NAME FROM INFORMATION_SCHEMA.TABLE_CONSTRAINTS WHERE TABLE_SCHEMA = 'PUBLIC';
+> CONSTRAINT_TYPE TABLE_NAME
+> --------------- ----------
+> PRIMARY KEY     TEST1
+> PRIMARY KEY     TEST2
+> rows: 2
+
+DROP TABLE TEST1, TEST2, TEST3;
+> ok