A New York City woman was arrested by federal authorities who said she tried to scam donors by posing as a relative of one of the children killed at a Connecticut elementary school. Nouel Alba, 37, was arrested Thursday and charged with lying to FBI agents. Federal prosecutors said she used her Facebook account, telephone calls, and text messages to seek donations for what she called a ‘‘funeral fund.’’ Authorities said Alba denied seeking the donations when she was contacted by FBI agents investigating charity scams related to the shooting at Sandy Hook Elementary School in Newtown. A gunman killed 20 children and six adults there on Dec. 14. Alba, of the Bronx, appeared Thursday in federal court in Hartford and was released on $50,000 bond.